These are some of the parallels from Melchizedeck priesthood that forshadowed the deliverer, Messiah to come Jesus.
No beginning/ no end, Jesus the Alpha and the Omega.
Priestly King/, Jesus our High Priest and King. (there have only been a few priestly kings recorded in the bible, but Jesus fulfilled the order according to the priesthood of Melchizedeck).
Offer sacrifices in form of bread and wine to God. Jesus fulfills both the bread and wine sacrifice in the Eucharist, and also the lamb sacrifice in his body and blood in his passsion, that is transubstantiated in the Eucharist, thus Jesus fulfilled every letter of the law and the prophets.
King of Salem, now Jerusalem, Jesus was crucified with the label “The King of the Jews” at his crucifixion from the worldly power.
It was prophesied that all animal sacrifices will cease, and the only acceptable sacrifice that God will accept, will be in the sacrifice according to the order of Melchizedeck, which Jesus does when he instituted the Eucharist to be his body and blood in the form of bread and wine, according to the priesthood of Melchizedeck.
Secondly Jesus being the new High Priestly/King of God, now institutes an everlasting priesthood, that will never end, That fulfills the last prophecy of Malachi, that today in the Catholic church from the rising of the sun to its setting the Catholic church offers daily an acceptable offering and sacrifice to God according to the order of Melchizedeck, in the form of bread and wine which are truly the body, blood, soul and divinity of Jesus Christ.
The following prophecy is fulfilled in Jesus, and it is only in the Catholic Church that has a valid sacrifice to offer to God that is acceptable and is excecuted daily in the sacrificial Mass of the Catholic church, which Jesus built on Peter, present day Pope Benedict 16th with unbroken succession. Jesus institutes his New Priesthood to the apostles at the last Supper. And when ever there is a change in the High Priesthood of God, there is a change of Law Covenant. Jesus institutes the New and everlasting Covenant in his body and blood, that God has prepared a body for him. This is why the Eucharist is always an acceptable Sacrifice unto God, because it is fully divine and fully human, not made by human hands, but from God. This is a great mystery that can be seen with the eyes of faith and trust in God’s holy Word, when he commands his church to eat his body and drink his blood (see John 6). For Catholics “faith is the realization of what is hoped for and evidence of things not seen”, That is why “it is the Spirit that gives life while the flesh is of no avail”
Malachi 1:11
For from the rising of the sun, even to its setting, my name is great among the nations; And everywhere they bring sacrifice to my name, and a pure offering; For great is my name among the nations, says the LORD of hosts.
In summary, the eternal Priesthood of Jesus is made according to the order of Melchizedeck, with no beginning and no end, sacrifice acceptable to God in the form of bread and wine. God is faithful to his Word. Jesus is not Melchizedeck, Jesus is our eternal High Priest/King according to the order of Melchizedeck, who is standing in heaven as a lamb as though slain, this is Jesus offering his sacrifice for all humanity in the presence of God. That main point is the family of the HighPriest/King has to consume the acceptabel sacrifice offered to God, this the Catholic church does daily, and communes with the Father in heaven to share in the New Covenant meal. There has never been a covenant without a meal shared.