Subset Relation is Antisymmetric

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