Projection is Epimorphism

Theorem
Let $\left({S, \circ}\right)$ be the external direct product of the algebraic structures $\left({S_1, \circ_1}\right)$ and $\left({S_2, \circ_2}\right)$.

Then:
 * $\operatorname{pr}_1$ is an epimorphism from $\left({S, \circ}\right)$ to $\left({S_1, \circ_1}\right)$
 * $\operatorname{pr}_2$ is an epimorphism from $\left({S, \circ}\right)$ to $\left({S_2, \circ_2}\right)$

where $\operatorname{pr}_1$ and $\operatorname{pr}_2$ are the first and second projection respectively of $\left({S, \circ}\right)$.