There can be no doubt in studying the primitive Church that the priesthood developed from this origin. The proof of the distinct priesthood rests upon the cross of Calvary. If what Jesus did from the Cross was an atoning sacrifice for mankind and if the Eucharist is the ongoing sacrifice of the Mass then it is necessary for a sacerdotal ecclesiastical priesthood as sacrifice and priesthood are terms that depend on one another throughout the Scriptures. The priesthood gains its veracity from the fact that the Eucharist is a part of the Church from the beginning making it a necessary part of the Church.
We can see the prophecy of the sacerdotal priesthood of the New Covenant in the writings of the prophet Isaiah. He teaches that in the Messianic Kingdom that priests will be called even from among the non-Jews which sets apart the New Covenant Church from the Old Covenant priesthood.
Isaiah 66:21 (King James Version)
21And I will also take of them for priests and for Levites, saith the LORD.
This priesthood is to fulfill the prophesy of Malachi for a permanent and continuous sacrifice:
Malachi 1:11 (King James Version)
11For from the rising of the sun even unto the going down of the same my name shall be great among the Gentiles; and in every place incense shall be offered unto my name, and a pure offering: for my name shall be great among the heathen, saith the LORD of hosts.
The following verses refer to the sacrifice of the bread and the wine by Melchisedec which scholars agree is the prototype of Christ. This also refers to the last supper where Jesus orders the repetition of the Mass.
Genesis 14:18 (New King James Version)
18 Then Melchizedek king of Salem brought out bread and wine; he was the priest of God Most High.
Hebrews 5:5-10 (King James Version)
5So also Christ glorified not himself to be made an high priest; but he that said unto him, Thou art my Son, to day have I begotten thee.
6As he saith also in another place, Thou art a priest for ever after the order of Melchisedec.
7Who in the days of his flesh, when he had offered up prayers and supplications with strong crying and tears unto him that was able to save him from death, and was heard in that he feared;
8Though he were a Son, yet learned he obedience by the things which he suffered;
9And being made perfect, he became the author of eternal salvation unto all them that obey him;
10Called of God an high priest after the order of Melchisedec.
So, it can be and has been said that the Church has received the ongoing sacrifice of our Lord and that as a result there is a sacerdotal priesthood necessarily separate from the priesthood of all believers that offers this continuous sacrifice to the Father of the Eucharist. As a result the priesthood has been changed by Christ and His sacrifice from the Old Covenant priesthood into the one prophesied in Scriptures by the prophets Isaiah and Malachi. So, in conclusion, if the sacrifice of Jesus on the cross was a atoning sacrifice for mankind then the priesthood is undeniable the priesthood prophesied and made necessary by Christ. We find this evidence in the colloquy of Capernaum and in the Gospel accounts of the last Supper. God bless!