Factor of is transitive test

Prove:

$((\forall X) \land (X \in integers) \land (\forall Y) \land (Y \in integers) \land (\forall Z) \land (Z \in integers) \land factor (X, Y) \land factor (Y, Z) \Rightarrow factor (X, Z))$

Given:

Axiom	Definition
factor	$(\forall X) \land (X \in integers) \land (\forall Y) \land (Y \in integers) \land factor (X, Y) \Leftrightarrow (\exists Z) \land (Z \in integers) \land ((X * Z) = Y)$