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 $$pr_j$$ on the $$j$$th co-ordinate is an epimorphism from $$G$$ onto $$G_j$$.