Subset Relation is Antisymmetric

Theorem
The subset relation is antisymmetric:


 * $\paren {x \subseteq y} \land \paren {y \subseteq x} \iff x = y$

where $x$ and $y$ are sets.

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