Natural Number is Union of its Successor

Theorem
Let $n \in \N$ be a natural number as defined by the von Neumann construction.

Then:
 * $\map \bigcup {n^+} = n$

Proof
From Natural Number is Superset of its Union we have:
 * $\bigcup n \subseteq n$

Then from Union with Superset is Superset‎:
 * $\bigcup n \subseteq n \iff \paren {n \cup \bigcup n} = n$

and the result follows.