# Category:Axioms/Axiom of Extension

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This category contains axioms related to Axiom of Extension.

### Set Theory

Let $A$ and $B$ be sets.

The **Axiom of Extension** states that:

- $A$ and $B$ are equal

- they contain the same elements.

That is, if and only if:

and:

This can be formulated as follows:

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

### Class Theory

The **axiom of extension** in the context of class theory has the same form:

Let $A$ and $B$ be classes.

Then:

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

## Pages in category "Axioms/Axiom of Extension"

The following 10 pages are in this category, out of 10 total.

### E

- Axiom:Axiom of Extension
- Axiom:Axiom of Extension (Classes)
- Axiom:Axiom of Extension (Sets)
- Axiom:Axiom of Extension/Also known as
- Axiom:Axiom of Extension/Class Theory
- Axiom:Axiom of Extension/Set Theory
- Axiom:Axiom of Extension/Set Theory/Formulation 1
- Axiom:Axiom of Extension/Set Theory/Formulation 2
- Axiom:Axiom of Extensionality
- Axiom:Axiom of Extent