Definition:Class Equality/Definition 1
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Definition
Let $A$ and $B$ be classes.
$A$ 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.
Sources
- 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 4.5$