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 $$\left({S_2, \circ_2}\right)$$.


 * $$pr_1$$ is an epimorphism from $$\left({S, \circ}\right)$$ to $$\left({S_1, \circ_1}\right)$$;
 * $$pr_2$$ is an epimorphism from $$\left({S, \circ}\right)$$ to $$\left({S_2, \circ_2}\right)$$.

where $$pr_1$$ and $$pr_2$$ are the first and second projection of $$\left({S, \circ}\right)$$.