## The quotient of a product is module isomorphic to the product of quotients

Let $R$ be a ring, let $\{A_i\}_{i=1}^n$ be a finite family of (left, unital) $R$-modules, and let $B_i \subseteq A_i$ be a submodule for each $i$. Prove that $(\prod A_i)/(\prod B_i) \cong_R \prod A_i/B_i$.

We did this previously. D&F, why repeat an exercise?