Cartesian Product is Small

Theorem
Let $a$ and $b$ be small classes.

Then their Cartesian product $a \times b$ is small:


 * $\map {\mathscr M} {a \times b}$

Proof
So by definition of power set:
 * $a \times b \subseteq \powerset {\powerset {a \cup b} }$

By Union of Small Classes is Small, $a \cup b$ is small.

By the Axiom of Powers, $\powerset {\powerset {a \cup b} }$ is small.

By Axiom of Subsets Equivalents, $a \times b$ is small.