# Axiom:Axiom of Pairing/Set Theory/Strong Form

## Axiom

For any two sets, there exists a set to which only those two sets are elements:

$\forall a: \forall b: \exists c: \forall z: \paren {z = a \lor z = b \iff z \in c}$

That is, let $a$ and $b$ be sets.

Then there exists a set $c$ such that $c = \set {a, b}$.

Thus it is possible to create a set whose elements are two sets that have already been created.

## Also known as

The axiom of pairing is also known as the axiom of the unordered pair.

Some sources call it the pairing axiom.