I think that is an oral tradition that you believe. As far as I know, none of the New Testament texts claim to be inerrant. And the list of books that belong in the N.T.--which is called the New Testament Canon--is not given in Scripture. The only historic source of this authoritative list is the Tradition of the Catholic Church.
How about a claim to be on par with what you consider to be inerrant? Do you not consider scripture to be inerrant? If so, then an NT claim to being on par with, or to actually BE scripture should suffice, yes?
Brace for incoming!(lol)
1Cor14:
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37] If any man think himself to be a prophet, or spiritual, let him acknowledge that the things that I write unto you are the commandments of the Lord.
Eph3
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3] How that by revelation he made known unto me the mystery; (as I wrote afore in few words,
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4] Whereby, when ye read, ye may understand my knowledge in the mystery of Christ)
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5] Which in other ages was not made known unto the sons of men, as it is now revealed unto his holy apostles and prophets by the Spirit;
Gal1:
11] But I certify you, brethren, that the gospel which was preached of me is not after man.
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12] For I neither received it of man, neither was I taught it, but by the revelation of Jesus Christ.
I checked those out personally for you, but the article I am looking in for them also had this to say if you need more:
Thessalonians 4:8 - The message was originated by God, not by the men who penned it (v2). So, those who reject it are rejecting, not the men, but God.
2 Timothy 3:16,17 -
All Scripture is inspired by God: not just the Old Testament, but all of it. It is profitable for teaching, reproof, instruction in righteousness and to provide us to all good works. In short, Scripture is what we claim it to be: a revelation of God's will to teach us how to live our lives. But is the New Testament "Scripture"?
1 Timothy 5:18 - The same writer quotes two passages that he calls "Scripture." One is from the Old Testament, and the other is from Luke 10:7. So, the New Testament is "Scripture" just like the Old Testament, and both are cited as authority that proves what we ought to practice.
2 Peter 3:15,16 - Peter referred to Paul's epistles as "Scripture," right along with other Scripture. We can appreciate the significance of this only when we understand what Peter and other inspired men mean by "Scripture." This same apostle, in 1:19-21, said Scriptures come from God, not man.
[2 Thessalonians 2:13-15; 3:14; Revelation 1:11,19,9; 22:18,19; chap. 2,3; 14:13; 19:9; 21:5; Acts 15:22-29; 16:4,5; 1 Peter 5:12; 1 John 2:7-17,21,26; 2 John 5]