Absolute Value Function is Completely Multiplicative/Proof 3

Theorem
Let $x, y \in \R$ be real numbers.

Let $\left\vert{x}\right\vert$ be the absolute value of $x$.

Then:
 * $\left\vert{xy}\right\vert = \left\vert{x}\right\vert \cdot \left\vert{y}\right\vert$