Existence of Singleton Set

Theorem
Let $a$ be a set.

Then the singleton set $\left\{{a}\right\}$ may be constructed.

Proof
Let $a$ be a set.

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

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