Set is Element of Successor

Theorem
Let $x$ be a set.

Let $x^+$ be the successor of $x$.

Then $x \in x^+$.

Proof
By the definition of successor set:


 * $x^+ = x \cup \{x\}$.

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

Thus by the definition of union, $x \in x^+$.