Restriction of Mapping is Subclass of Cartesian Product

Theorem
Let $V$ be a basic universe

Let $f: V \to V$ be a mapping.

Let $A$ be a class.

Let $f \sqbrk A$ denote the image of $A$ under $f$.

Let $f {\restriction} A$ denote the restriction of $f$ to $A$.

Then $f {\restriction} A$ is a subclass of the cartesian product of $A$ with its image:
 * $f {\restriction} A \subseteq A \times f \sqbrk A$

Proof
Follows directly from:
 * the definition of restriction
 * the definition of mapping.