Projection on Cartesian Product of Modules

Theorem
Let $G$ be the cartesian product of a sequence $\left \langle {G_n} \right \rangle$ of $R$-modules.

Then for each $j \in \left[{1 \,.\,.\, n}\right]$, the projection $\operatorname{pr}_j$ on the $j$th co-ordinate is an epimorphism from $G$ onto $G_j$.