Cartesian Product of Intersections

Theorem

 * $\paren {S_1 \cap S_2} \times \paren {T_1 \cap T_2} = \paren {S_1 \times T_1} \cap \paren {S_2 \times T_2}$

where $S_1, S_2, T_1, T_2$ are sets.