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As regards the oft-quoted Mt. 16:18, note the following bishops promise in the profession of faith of Vatican 1:

• Basil of Seleucia, Oratio 25:

'You are Christ, Son of the living God.'...Now Christ called this confession a rock, and he named the one who confessed it 'Peter,' perceiving the appellation which was suitable to the author of this confession. For this is the solemn rock of religion, this the basis of salvation, this the wall of faith and the foundation of truth: 'For no other foundation can anyone lay than that which is laid, which is Christ Jesus.' To whom be glory and power forever. — Oratio XXV.4, M.P.G., Vol. 85, Col. 296-297.

• Bede, Matthaei Evangelium Expositio, 3:

You are Peter and on this rock from which you have taken your name, that is, on myself, I will build my Church, upon that perfection of faith which you confessed I will build my Church by whose society of confession should anyone deviate although in himself he seems to do great things he does not belong to the building of my Church...Metaphorically it is said to him on this rock, that is, the Saviour which you confessed, the Church is to be built, who granted participation to the faithful confessor of his name. — 80Homily 23, M.P.L., Vol. 94, Col. 260. Cited by Karlfried Froehlich, Formen, Footnote #204, p. 156 [unable to verify by me].

• Cassiodorus, Psalm 45.5:

'It will not be moved' is said about the Church to which alone that promise has been given: 'You are Peter and upon this rock I shall build my Church and the gates of Hell shall not prevail against it.' For the Church cannot be moved because it is known to have been founded on that most solid rock, namely, Christ the Lord. — Expositions in the Psalms, Volume 1; Volume 51, Psalm 45.5, p. 455

• Chrysostom (John) [who affirmed Peter was a rock, but here not the rock in Mt. 16:18]:

Therefore He added this, 'And I say unto thee, Thou art Peter, and upon this rock I will build my Church; that is, on the faith of his confession. — Chrysostom, Homilies on the Gospel of Saint Matthew, Homily LIIl; Philip Schaff, Nicene and Post-Nicene Fathers (http://www.ccel.org/ccel/schaff/npnf110.iii.LII.html)

• Cyril of Alexandria:

When [Peter] wisely and blamelessly confessed his faith to Jesus saying, 'You are Christ, Son of the living God,' Jesus said to divine Peter: 'You are Peter and upon this rock I will build my Church.' Now by the word 'rock', Jesus indicated, I think, the immoveable faith of the disciple.”. — Cyril Commentary on Isaiah 4.2.

• Origen, Commentary on the Gospel of Matthew (Book XII):

“For a rock is every disciple of Christ of whom those drank who drank of the spiritual rock which followed them, 1 Corinthians 10:4 and upon every such rock is built every word of the church, and the polity in accordance with it; for in each of the perfect, who have the combination of words and deeds and thoughts which fill up the blessedness, is the church built by God.'

“For all bear the surname ‘rock’ who are the imitators of Christ, that is, of the spiritual rock which followed those who are being saved, that they may drink from it the spiritual draught. But these bear the surname of rock just as Christ does. But also as members of Christ deriving their surname from Him they are called Christians, and from the rock, Peters.” — Commentary on the Gospel of Matthew (Book XII), sect. 10,11 ( http://www.newadvent.org/fathers/101612.htm)

• Hilary of Potier, On the Trinity (Book II): Thus our one immovable foundation, our one blissful rock of faith, is the confession from Peter's mouth, Thou art the Son of the living God. On it we can base an answer to every objection with which perverted ingenuity or embittered treachery may assail the truth."-- (Hilary of Potier, On the Trinity (Book II), para 23; Philip Schaff, editor, The Nicene & Post Nicene Fathers Series 2, Vol 9.