# Axiom:Axiom of Powers/Class Theory

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## Axiom

Let $x$ be a set.

Then its power set $\powerset x$ is also a set.

## Also known as

The **axiom of powers** is also known as:

- the
**axiom of the power set** - the
**power set axiom**

## Also see

- Results about
**Axiom of Powers**can be found here.

## 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: $\S 6$ The power axiom: $A_6$**[Power set axiom]**

*although there exists a misprint: it is referred to as the***Power aet axiom**.