Non-Zero Integers are Cancellable for Multiplication/Proof 2

Theorem
Every non-zero integer is cancellable for multiplication.

That is:
 * $\forall x, y, z \in \Z, x \ne 0: x y = x z \iff y = z$

Proof
Let $y, z \in \Z: y \ne z$.

The result follows by transposition.