With all due respect, I don’t see how all of the Apostles and their successor bishops are all successors of Saint Peter.
St Cyprian of Carthage, in “On the Unity of the Church” (the longer version), refers to the keys, stating that Peter received them on behalf of the Twelve, and that the bishops, being successors of the twelve, are all heirs of the keys, because the episcopal order is a single, undivided entity. Hence, the power of the keys belongs to ALL bishops, and not merely the bishop of Rome.
St. Augustine
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For these keys not one man but the unity of the Church received. Hereby, then, is the excellence of Peter set forth that he was an emblem of the Church in its universality and unity, when it was said to him,
I give to thee what was given to all. For that ye may know that the Church did receive the keys of the kingdom of heaven hear in another place what the Lord said to all Apostles. “Receive the Holy Ghost,” and then instantly, “whosoever sins ye remit they are remitted unto them, and whosoever sins ye retain they are retained”[St. John xx. 22,23].
St. Jerome
“But you say that the Church is founded on Peter, although the same thing is done in another place upon all the Apostles,
and all receive the keys of the kingdom of heaven, and the solidity of the Church is established equally upon all.”[see: S. Hieron., Adv. Jovin. i. cap. xxvi.; P.L. xxiii. 247].
St. Ambrose
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therefore the Lord gave the Apostles that which was previously part of his own juridical authority. Hear Him saying I will give the keys of the Kingdom of heaven; whatsoever thou shalt bind on earth shall be bound in heaven, and whatsoever thou shalt loose on earth shall be loosed in heaven, to thee he says, I will give the keys of the Kingdom of heaven, that you may bind and loose.
What he said to peter is said to the Apostles.”[St. Ambrose, Enarratio in Psalm. xxxviii. 37; P.L. xiv. 1037].
ZP