# Category:Class Equality

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This category contains results about **Class Equality**.

Definitions specific to this category can be found in Definitions/Class Equality.

Let $A$ and $B$ be classes.

### Definition 1

$A$ and $B$ are **equal**, denoted $A = B$, if and only if:

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

where $\in$ denotes class membership.

### Definition 2

$A$ and $B$ are **equal**, denoted $A = B$, if and only if:

- $A \subseteq B$ and $B \subseteq A$

where $\subseteq$ denotes the subclass relation.