Bertrand Russell proved it via set theory [1]. Which is again based on the axioms of set theory, so as repsilat said above, you end up in one of the Münchhausen trilemmae, in this case you end up in some mix of regressive and axiomatic argument: there's an axiom, you cannot prove it within itself, but with another axiom and so forth.

It's a difficult subject and I am by no means an expert in it.

[1] https://blog.plover.com/math/PM.html

PS: You are correct, 1+1=2 is not a tautology. With a tautology, both the statement and the negation of the statement are true. In this case either 1+1=2 or 1+1=!2 - but never both, if you get what I mean?

PPS: And sorry for all those downvotes - don't understand why. Your questions are perfectly fine.