Verse 23 references Deuteronomy 18:15: “The Lord thy God will raise up unto thee a Prophet from the midst of thee, of thy brethren, like unto me; unto him ye shall hearken.” Luke, the writer of the book of Acts in the New Testament, referenced this scripture in Acts 3:22 and 7:37. Nephi (son of Lehi) referenced that verse in 1 Nephi 22:20.
It happens with some frequency that during the translation process, Joseph Smith would quote an Old Testament scripture, but the version of that scripture as it appears in the New Testament. That is the case here, and we can tell that, as a translator, it was Acts 3:22 that he had in mind. Notice the similarity between verses 24-26 of 3 Nephi 20, and Acts 3:24-26: “Yea, and all the prophets from Samuel and those that follow after, as many as have spoken, have likewise foretold of these days. Ye are the children of the prophets, and of the covenant which God made with our fathers, saying unto Abraham, And in thy seed shall all the kindreds of the earth be blessed. Unto you first God, having raised up his Son Jesus, sent him to bless you, in turning away every one of you from his iniquities.”
The use of these more familiar verses to provide the text that was intended is one of the methods that Joseph used to translate the Book of Mormon. The intent of Jesus’s words was to declare himself the fulfillment of prophecy, something that those who had been with him the day before had learned, but is being repeated for those who arrived more recently. The use of passages familiar to the readers of the Book of Mormon that translated the intent of the Nephite words occurs several times, and simply indicates that the purpose of the translation was to speak to the modern audience rather than the ancient one.