Absolute Value Function is Completely Multiplicative/Proof 4

Theorem
The absolute value function on the real numbers $\R$ is completely multiplicative:


 * $\forall x, y: \left\vert{x y}\right\vert = \left\vert{x}\right\vert \, \left\vert{y}\right\vert$

where $\left \vert{a}\right \vert$ denotes the absolute value of $a$.

Proof
Follows directly from:
 * Real Numbers form Ordered Integral Domain
 * Product of Absolute Values on Ordered Integral Domain.