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>> “The Church of Rome has been around since Peter” <<
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No, it has been around since it was founded, in 364 AD.
(or do you trace it back to the serpent in the tree?)
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"See that you all follow the bishop, even as Jesus Christ does the Father, and the presbytery as you would the apostles; and reverence the deacons, as being the institution of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is administered either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude of the people also be; even as wherever Jesus Christ is, there is the Catholic Church [Gr. εκει η καθολικη εκκλησια].
St. Ignatius of Antioch, Epistle to the Smyrnaeans, Ch 8
So Wrong. The Church is mentioned in Scripture. Paul tells us to take issues to the Church. Paul tells us the Church is the pillar and foundation of Truth