Internal Group Direct Product Commutativity

Theorem
Let $\struct {G, \circ}$ be a group whose identity is $e$.

Let $H$ and $K$ be subgroups of $G$.

Let $\struct {G, \circ}$ be the internal group direct product of $H$ and $K$.

Then:
 * $\forall h \in H, k \in K: h \circ k = k \circ h$