# 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:

$\set {a, a} = \set a$

$\blacksquare$