If x * y = 0 then x or y is 0 test

Prove:

$((\forall X) \land (X \in integers) \land (\forall Y) \land (Y \in integers) \land ((X * Y) = 0) \Rightarrow ((X = 0) \lor (Y = 0)))$

Given:

Axiom	Definition
zero_times	$((\forall X) \land (X \in integers) \land ((X * 0) = 0))$
division	$((\forall X) \land (X \in integers) \land (\forall Y) \land (Y \in integers) \land (\forall Z) \land (Z \in integers) \land ((X * Y) = (X * Z)) \land (X \neq 0) \Rightarrow (Y = Z))$