The prophecy of Moses is from the book of Deuteronomy, which is worded slightly different than Nephi’s, but is the same meaning.
18 I will raise them up a Prophet from among their brethren, like unto thee, and will put my words in his mouth; and he shall speak unto them all that I shall command him.
19 And it shall come to pass, that whosoever will not hearken unto my words which he shall speak in my name, I will require it of him. [Deuteronomy 18:18–19]
Nephi’s identification of that prophet as “the Holy One of Israel” is the same as given by the Apostle Peter in the New Testament.
20 And he shall send Jesus Christ, which before was preached unto you:
21 Whom the heaven must receive until the times of restitution of all things, which God hath spoken by the mouth of all his holy prophets since the world began.
22 For Moses truly said unto the fathers, A prophet shall the Lord your God raise up unto you of your brethren, like unto me; him shall ye hear in all things whatsoever he shall say unto you.
23 And it shall come to pass, that every soul, which will not hear that prophet, shall be destroyed from among the people. [Acts 3:20–23]
Peter’s words are also slightly different, but the same message. The differences are probably because of the translation from different languages. Both Peter and Nephi use the prophecy as a latter-day event, although the Deuteronomy text speaks of the prophet (Christ) being raised up. Wherefore, being raised up may have reference to the Lord’s appearance. Jesus paraphrased this prophecy to the Nephites.
11 Therefore it shall come to pass that whosoever will not believe in my words, who am Jesus Christ, which the Father shall cause him to bring forth unto the Gentiles, and shall give unto him power that he shall bring them forth unto the Gentiles, (it shall be done even as Moses said) they shall be cut off from among my people who are of the covenant. [3 Nephi 21:11]
The Book of Mormon contains the words of Jesus that are to be brought to the Nephites. Those who reject it will be cut off. Therefore, the prophecy of Moses will not be fulfilled until the Book of Mormon has been sent “to every nation, and kindred, and tongue, and people” as John the Revelator testified (Revelation 14:6).
As a further clarification of the meaning of being cut off from God’s people (gathered Israel), Nephi speaks of the fall of the kingdom of the devil. He enumerates those who are included in that kingdom (1 Nephi 22:22–23). All churches and their various characteristics means there are many churches, not just one. These many churches supports our earlier conclusion that the kingdom of the devil is not a single organization, but embraces all the organizations and teachings of evil that oppose the kingdom of God. This is similar to the admonition given to the Three Witnesses of the Book of Mormon “Contend against no church, save it be the church of the devil” (D&C 18:20).