Proper Class is not Element of Class
Jump to navigation
Jump to search
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 result follows by definition of a class.
$\blacksquare$