Textbook Problem

Prove each statement in 39-44.

For every positive integer n, if A and $B_1,B_2,B_{3,\mathrm{....}}$ are any set, then

${\displaystyle \underset{i=1}{\overset{n}{\cap }}\left(A\times B_i\right)=A\times \left({\displaystyle \underset{i=1}{\overset{n}{\cap }}{B}_i}\right).}$