Is this an axiom or a proof?
Neither. An axiom is in particular a proposition, i.e., something that is either true or false. Here, 1 + 1 - 2 is neither true nor false. Further, a proof is an expression that usually combines propositions according to specified inference rules. Therefore, this is not a proof, either.
Whether 1 + 1 = 2 is considered an axioms or a theorem varies between formal systems. E.g., in Peano Arithmetic, it is a theorem and in the Calculus of Inductive Constructions it is an (instance of a universal) axiom.