Cartesian Product of Intersections

Theorem

 * $\left({S_1 \cap S_2}\right) \times \left({T_1 \cap T_2}\right) = \left({S_1 \times T_1}\right) \cap \left({S_2 \times T_2}\right)$

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