Subset Relation is Antisymmetric

Theorem
The relation "is a subset of" is antisymmetric:


 * $\paren {R \subseteq S} \land \paren {S \subseteq R} \iff R = S$

Proof
This is a direct statement of the definition of set equality:
 * $R = S := \paren {R \subseteq S} \land \paren {S \subseteq R}$