Subset Relation is Antisymmetric

From ProofWiki
Jump to navigation Jump to search

Theorem

The relation "is a subset of" is antisymmetric:

$\left({R \subseteq S}\right) \land \left({S \subseteq R}\right) \iff R = S$


Proof

This is a direct statement of the definition of set equality:

$R = S := \left({R \subseteq S}\right) \land \left({S \subseteq R}\right)$

$\blacksquare$


Sources