Definition:Set Equality/Definition 1

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Two sets are equal if and only if they have the same elements.

This can be defined rigorously as:

$S = T \iff \paren {\forall x: x \in S \iff x \in T}$

where $S$ and $T$ are both sets.

Otherwise, $S$ and $T$ are distinct, or unequal.

Also see