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.