While Alma 13 is the most explicit evidence that the Nephites held the
Melchizedek Priesthood, there are other hints, including Lehi et al offering
sacrifices (a priestly action) which were accepted by God:
And it came to pass
that they did rejoice exceedingly, and did offer sacrifice and burnt offerings
unto the Lord; and they gave thanks unto the God of Israel. (1 Nephi 5:9)
And it came to pass
that we did come down unto the tent of our father. And after I and my brethren
and all the house of Ishmael had come down unto the tent of my father, they did
give thanks unto the Lord their God; and they did offer sacrifice and burnt offerings
unto him. (1 Nephi 7:22)
Another text would be Mosiah 2:3, which raises the question as to the
Nephite sacrificial system in light of there being no Levitical priests, something
addressed by Matthew P. Roper at: