# Axiom:Axiom of Pairing/Class Theory

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## Axiom

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

- Doubleton Class can be Formed from Two Sets, which demonstrates the fact that the class $\set {a, b}$ can be created in the first place

## Sources

- 2010: Raymond M. Smullyan and Melvin Fitting:
*Set Theory and the Continuum Problem*(revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 4$ The pairing axiom: $A_4$**[Pairing axiom]**