I think saying that a theorem is true presumes the axioms upon which it is based and so the entire system is “true everywhere forever”.

I often find it helpful to think of chess as my axiomatic system. When we say the king is in checkmate, it presumes that we accept all the underlying rules of chess. And these pieces that theoretically form a checkmate will always do so forever… Assuming the regular rules of chess, etc.

When you put things in terms of chess, these “deep” statements about “math” often become banal.