# Class is Proper iff Bijection from Class to Proper Class/Corollary

## Theorem

Let $A$ be a class.

Let $\mathrm P$ be a proper class.

Then $A$ is proper if and only if there exists a bijection from $\mathrm P$ to $A$.

## Proof

This page is beyond the scope of ZFC, and should not be used in anything other than the theory in which it resides.

There exists a bijection from $A$ to $\mathrm P$ iff there exists a bijection from $\mathrm P$ to $A$.
$\blacksquare$