# Axiom:Axiom of Pairing

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## Axiom

### Set Theory

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

- $\forall A: \forall B: \exists x: \forall y: \paren {y \in x \iff y = A \lor y = B}$

Thus it is possible to create a set that contains as elements any two sets that have already been created.

### 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.