# 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:

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

### 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**.

## Sources

- 2002: Thomas Jech:
*Set Theory*(3rd ed.) ... (previous) ... (next): Chapter $1$: Pairing