Cartesian Product Exists and is Unique

Theorem
Let $A$ and $B$ be classes.

Let $A \times B$ be the cartesian product of $A$ and $B$.

Then $A \times B$ exists and is unique.

Proof
By the Axiom of Specification, there exists a class $C$ such that:
 * $C = \set {\tuple {x, y} : x \in A \land y \in B}$

By definition, $C$ is the cartesian product of $A$ and $B$.

Thus $A \times B$ exists.

By Cartesian Product is Unique, $A \times B$ is unique.