Restriction of Mapping to Small Class is Small

Theorem
Let $F$ be a mapping.

Let $A$ be a small class.

Then the restriction $( F \restriction A )$ is a small class.

Proof
The domain of $( F \restriction A )$ is a subset of $A$.

By Axiom of Subsets Equivalents, the domain is a small class.

By Mapping is Small, it follows that $( F \restriction A )$ is a small class.