As I read Moses 5-6, there are three things which God promises (or decrees) to Adam that will be in the world from the beginning until the end. Those three things are 1) the Gospel, 2) a chosen seed that will always be preserved and will bless all the Families of the earth, and 3) the Priesthood. (With Abraham, the promise of a chosen seed that will bless all Families is slightly altered: his seed will be as innumerable as the stars or the sands on the shore, and everyone who believes the Gospel will be counted as his seed. Abraham also receives promises about an inheritance of specific land, which I’m not addressing here.)
Here are the passages from Moses 5-6 where those three promises are made initially, and some other significant passages throughout scripture that shed some light on those three promises.
1) The Gospel
Moses 5:7-8: And then the angel spake, saying: This thing is a similitude of the sacrifice of the Only Begotten of the Father, which is full of grace and truth. Wherefore, thou shalt do all that thou doest in the name of the Son, and thou shalt repent and call upon God in the name of the Son forevermore.
Moses 5:14-15: And the Lord God called upon men by the Holy Ghost everywhere and commanded them that they should repent; And as many as believed in the Son, and repented of their sins, should be saved; and as many as believed not and repented not, should be damned; and the words went forth out of the mouth of God in a firm decree; wherefore they must be fulfilled.
Moses 5:57-59: For they would not hearken unto his voice, nor believe on his Only Begotten Son, even him whom he declared should come in the meridian of time, who was prepared from before the foundation of the world. And thus the Gospel began to be preached, from the beginning, being declared by holy angels sent forth from the presence of God, and by his own voice, and by the gift of the Holy Ghost. And thus all things were confirmed unto Adam, by an holy ordinance, and the Gospel preached, and a decree sent forth, that it should be in the world, until the end thereof; and thus it was. Amen.
Moses 6:29-30: and a hell I have prepared for them, if they repent not; And this is a decree, which I have sent forth in the beginning of the world, from my own mouth, from the foundation thereof, and by the mouths of my servants, thy fathers, have I decreed it, even as it shall be sent forth in the world, unto the ends thereof.
Enoch teaches it: Moses 6:51-52 and elsewhere; Noah teaches it Moses 8:19, for example (And the Lord ordained Noah after his own order, and commanded him that he should go forth and declare his Gospel unto the children of men, even as it was given unto Enoch.)
2) Chosen seed who will bless all Families / Seed Multiplied / Seed not destroyed:
Moses 5:10-11 (I don’t understand what this has to do with the families of the earth, but verse 10 links it, so I’m including the reference until I figure it out)
Moses 6:2 And Adam knew his wife again, and she bare a son, and he called his name Seth. And Adam glorified the name of God; for he said: God hath appointed me another seed, instead of Abel, whom Cain slew.
Moses 6:8: and a genealogy was kept of the children of God. And this was the book of the generations of Adam, saying: In the day that God created man, in the likeness of God made he him…
Moses 6:22-23: And this is the genealogy of the sons of Adam, who was the son of God, with whom God, himself, conversed. And they were preachers of righteousness, and spake and prophesied, and called upon all men, everywhere, to repent; and faith was taught unto the children of men.
Also D&C 107:40-42: …the literal descendants of the chosen seed, to whom the promises were made. This order was instituted in the days of Adam, and came down by lineage in the following manner: From Adam to Seth, who was ordained by Adam at the age of sixty-nine years, and was blessed by him three years previous to his (Adam’s) death, and received the promise of God by his father, that his posterity should be the chosen of the Lord, and that they should be preserved unto the end of the earth;
Moses 7:50-53: And the Lord could not withhold; and he covenanted with Enoch, and sware unto him with an oath, that he would stay the floods; that he would call upon the children of Noah; And he sent forth an unalterable decree, that a remnant of his seed should always be found among all nations, while the earth should stand
Moses 8:2 And it came to pass that Methuselah, the son of Enoch, was not taken, that the covenants of the Lord might be fulfilled, which he made to Enoch; for he truly covenanted with Enoch that Noah should be of the fruit of his loins.
JST Genesis 9:14-15: And God spake unto Noah, and to his sons with him, saying, And I, behold, I will establish my covenant with you, which I made unto your father Enoch, concerning your seed after you.
Abraham 1:4: I sought for mine appointment unto the Priesthood according to the appointment of God unto the fathers concerning the seed.
Abraham 1:19: As it was with Noah so shall it be with thee; but through thy ministry my name shall be known in the earth forever, for I am thy God.
JST Genesis 17:8-9 (to Abraham): But as for thee, behold, I will make my covenant with thee, and thou shalt be a father of many nations. And this covenant I make, that thy children may be known among all nations.
Genesis 22:17-18 (to Abraham, after Isaac’s sacrifice): That in blessing I will bless thee, and in multiplying I will multiply thy seed as the stars of the heaven, and as the sand which is upon the sea shore; and thy seed shall possess the gate of his enemies; And in thy seed shall all the nations of the earth be blessed; because thou hast obeyed my voice.
Genesis 26:3-5 (to Isaac): And I will make thy seed to multiply as the stars of heaven, and will give unto thy seed all these countries; and in thy seed shall all the nations of the earth be blessed;
Genesis 28:14 (to Jacob): And thy seed shall be as the dust of the earth, and thou shalt spread abroad to the west, and to the east, and to the north, and to the south: and in thee and in thy seed shall all the families of the earth be blessed.
Genesis 49:25-26 (Jacob to Joseph): The blessings of thy father have prevailed above the blessings of my progenitors unto the utmost bound of the everlasting hills: they shall be on the head of Joseph, and on the crown of the head of him that was separate from his brethren.
2 Nephi 3:16 (to Joseph): Yea, thus prophesied Joseph: I am sure of this thing, even as I am sure of the promise of Moses; for the Lord hath said unto me, I will preserve thy seed forever.
Exodus 32:9-14: And the Lord said unto Moses, I have seen this people, and, behold, it is a stiffnecked people: Now therefore let me alone, that my wrath may wax hot against them, and that I may consume them: and I will make of thee a great nation. And Moses besought the Lord his God … Remember Abraham, Isaac, and Israel, thy servants, to whom thou swarest by thine own self, and saidst unto them, I will multiply your seed as the stars of heaven, and all this land that I have spoken of will I give unto your seed, and they shall inherit it for ever. And the Lord repented of the evil which he thought to do unto his people.
ISAIAH. (Basically, the whole book.) For example, Isaiah 61:9: And their seed shall be known among the Gentiles, and their offspring among the people: all that see them shall acknowledge them, that they are the seed which the Lord hath blessed.
2 Nephi 3:23 (Lehi to Joseph): Wherefore, because of this covenant thou art blessed; for thy seed shall not be destroyed, for they shall hearken unto the words of the book.
D&C 68:8-11 (to Joseph Smith): Therefore, thus saith the Lord unto you, with whom the priesthood hath continued through the lineage of your fathers— For ye are lawful heirs, according to the flesh, and have been hid from the world with Christ in God— Therefore your life and the priesthood have remained, and must needs remain through you and your lineage until the restoration of all things spoken by the mouths of all the holy prophets since the world began. Therefore, blessed are ye if ye continue in my goodness, a light unto the Gentiles, and through this priesthood, a savior unto my people Israel. The Lord hath said it. Amen.
D&C 128: 18: …It is sufficient to know, in this case, that the earth will be smitten with a curse unless there is a welding link of some kind or other between the fathers and the children, upon some subject or other…
D&C 132: 30-31 (to Joseph Smith): Abraham received promises concerning his seed, and of the fruit of his loins—from whose loins ye are, namely, my servant Joseph—which were to continue so long as they were in the world; and as touching Abraham and his seed, out of the world they should continue; both in the world and out of the world should they continue as innumerable as the stars; or, if ye were to count the sand upon the seashore ye could not number them. This promise is yours also, because ye are of Abraham, and the promise was made unto Abraham; and by this law is the continuation of the works of my Father, wherein he glorifieth himself.
D&C 132:34: God commanded Abraham, and Sarah gave Hagar to Abraham to wife. And why did she do it? Because this was the law; and from Hagar sprang many people. This, therefore, was fulfilling, among other things, the promises.
Moses 6:7-8: Now this same Priesthood, which was in the beginning, shall be in the end of the world also. Now this prophecy Adam spake, as he was moved upon by the Holy Ghost, and a genealogy was kept of the children of God.
D&C 107:39-58: It is the duty of the Twelve, in all large branches of the church, to ordain evangelical ministers, as they shall be designated unto them by revelation— The order of this priesthood was confirmed to be handed down from father to son, and rightly belongs to the literal descendants of the chosen seed, to whom the promises were made. This order was instituted in the days of Adam, and came down by lineage in the following manner…
Matthew 16:18-19: And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it. And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven; and whatsoever thou shalt loose on earth shall be loosed in heaven.
D&C 84:6-17: And the sons of Moses, according to the Holy Priesthood which he received under the hand of his father-in-law, Jethro; And Jethro received it under the hand of Caleb; … Esaias also lived in the days of Abraham, and was blessed of him— Which Abraham received the priesthood from Melchizedek, who received it through the lineage of his fathers, even till Noah; … father Adam, who was the first man— Which priesthood continueth in the church of God in all generations, and is without beginning of days or end of years.
D&C 128:9 It may seem to some to be a very bold doctrine that we talk of—a power which records or binds on earth and binds in heaven. Nevertheless, in all ages of the world, whenever the Lord has given a dispensation of the priesthood to any man by actual revelation, or any set of men, this power has always been given.
D&C 132:7: …and I have appointed unto my servant Joseph to hold this power in the last days, and there is never but one on the earth at a time on whom this power and the keys of this priesthood are conferred…