Projection on Group Direct Product is Epimorphism/Proof 1

Proof
From Projection is Surjection, $\pr_1$ and $\pr_2$ are surjections.

We now need to show they are homomorphisms.

Let $g, h \in \struct {G, \circ}$ where $g = \tuple {g_1, g_2}$ and $h = \tuple {h_1, h_2}$.

Then:

and thus the morphism property is demonstrated for both $\pr_1$ and $\pr_2$.