Existence of Singleton Set

Theorem
Let $a$ be a set.

Then the singleton set $\set a$ may be constructed such that.
 * $a \in \set a$

Proof
Let $a$ be a set.

From the Axiom of Pairing the set $\set {a, a}$ may be formed.

From the Axiom of Extension it follows that:
 * $\set {a, a} = \set a$