# Axiom:Axiom of Pairing

## Axiom

### Set Theory

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

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

### Class Theory

Let $a$ and $b$ be sets.

Then the class $\set {a, b}$ is likewise a set.

## Also known as

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

Some sources call it the pairing axiom.

## Also see

• Results about the axiom of pairing can be found here.