Product of Integral Multiples

Theorem
Let $\struct {F, +, \times}$ be a field.

Let $a, b \in F$ and $m, n \in \Z$.

Then:
 * $\paren {m \cdot a} \times \paren {n \cdot b} = \paren {m n} \cdot \paren {a \times b}$

where $m \cdot a$ is as defined in Integral Multiple.