Definition:Class Equality/Definition 1

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: $\S 4.5$