# Proper Class is not Element of Class

## Theorem

Let $\mathrm P$ be a proper class.

Then $\mathrm P$ is not an element of any class, that is:

$\neg \exists A : \mathrm P \in A$

## Proof

From the definition of a proper class, $\mathrm P$ is not a set.

The rest then follows from the definition of a class.

$\blacksquare$