Subset Relation is Antisymmetric

Theorem
The subset relation is antisymmetric:


 * $\paren {A \subseteq B} \land \paren {B \subseteq A} \iff A = B$

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