Cartesian Product of Intersections/Corollary 2

Corollary to Cartesian Product of Intersections

 * $\paren {A \times B} \cap \paren {B \times A} = \paren {A \cap B} \times \paren {A \cap B}$

Proof
Take the result Cartesian Product of Intersections:
 * $\paren {S_1 \cap S_2} \times \paren {T_1 \cap T_2} = \paren {S_1 \times T_1} \cap \paren {S_2 \times T_2}$

Put $S_1 = A, S_2 = B, T_1 = B, T_2 = A$: