Theorem
Foundations and logic
A statement established by a valid deductive proof from stated axioms together with previously proved results.
What is usually left out
Theoremhood is relative to an axiom system, not absolute. A statement can be a theorem of one system and independent of a weaker one — the well-ordering theorem is a theorem of ZFC but not of ZF alone. Saying a theorem is "proved true" quietly conflates provability with truth, which is exactly the distinction Gödel’s theorems turn on.