Cartesian Product of Intersections/Corollary 1

Corollary

 * $A \times \left({B \cap C}\right) = \left ({A \times B}\right) \cap \left ({A \times C}\right)$

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

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