Category:Definitions/Class Equality

This category contains definitions related to Class Equality.
Related results can be found in Category: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.