Product set/Intersection/2/Exercise

Let ${}M$ and ${}N$ denote sets and let ${}A_{1},A_{2}\subseteq M$ and ${}B_{1},B_{2}\subseteq N$ be subsets. Show the identity

${}{\left(A_{1}\times B_{1}\right)}\cap {\left(A_{2}\times B_{2}\right)}={\left(A_{1}\cap A_{2}\right)}\times {\left(B_{1}\cap B_{2}\right)}\,.$

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