# Math Help - proof about subsets and intersections

1. ## proof about subsets and intersections

If A is a subset of B and C is a subset of D, then A intersect C is a subset of B intersect D.

Please any help in proving this conditional would be much appreciated

Suppose that $x\in{A\cap\\C}$. Then, $x\in{A}$ and $x\in{C}$. Since $A\subset{B}$, $x\in{B}$ and, because $C\subset{D}$, $x\in{D}$ as well. Thus, $x\in{B\cap{D}}$.