Inverse of Small Relation is Small

Theorem
Let $a$ be a small class.

Let $a$ also be a relation.

Then the inverse relation of $a$ is small.

Proof
Let $A$ equal:


 * $\set {\tuple {\tuple {x, y}, \tuple {y, x} } : \tuple {x, y} \in a}$

Then $A$ maps $a$ to its inverse.

Thus, the inverse of $a$ is the image of $a$ under $A$.

By Image of Small Class under Mapping is Small, the inverse of $a$ is small.