ThmDex – An index of mathematical definitions, results, and conjectures.

Result R2741 on D78: Subset

Set equality iff inclusion in both directions

Formulation 0

Let $X$ and $Y$ each be a D11: Set.

Then $X = Y$ if and only if

(1)	\begin{equation} X \subseteq Y \end{equation}
(2)	\begin{equation} X \supseteq Y \end{equation}