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:


 * $\left\{ \left({ \left({ x,y }\right), \left({ y,x }\right) }\right) : \left({ x,y }\right) \in a \right\}$

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.