User:Dfeuer/Empty Set does not Equal its Singleton

Theorem

Let $\varnothing$ be the empty class.

Let $\{\varnothing\}$ be singleton $\varnothing$.

Then $\varnothing ≠ \{\varnothing\}$.

Proof

By the definition of singleton, $\varnothing \in \{\varnothing\}$.

However, $\forall x: x \notin \varnothing$.

Thus $\varnothing ≠ \{\varnothing\}$.

$\blacksquare$