Mixed Volume And Containment

Show that if polytopes $P_1, \dots, P_n, Q_1, \dots, Q_n$ in $\mathbb{R}^n$ are such that $P_i \subset Q_i$ for all $i=1,\dots,n$, then
$$�3�\text{MV}(P_1,\dots,P_n) \leq \text{MV}(Q_1,\dots,Q_n).�4�$$