User:Dfeuer/Zero has no Predecessor

Theorem
Let $a$ be a set.

Then $a^+ ≠ 0$.

Proof
By definition, $a^+ = a \cup \{a\}$.

By definition, $0 = \varnothing$.

By the definition s of union and singleton, $a \in a^+$.

By the definition of the empty class, $a \notin 0$.

Thus $a^+ ≠ 0$.