User:Dfeuer/Zero has no Predecessor
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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 $a^+ ≠ 0$.
$\blacksquare$