Definition:Class Equality/Definition 2

Definition

Let $A$ and $B$ be classes.

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

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

where $\subseteq$ denotes the subclass relation.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 1$ Extensionality and separation