Associativity of Operation in Group Direct Product/Proof 2

Theorem
Let $\left({G \times H, \circ}\right)$ be the group direct product of the two groups $\left({G, \circ_1}\right)$ and $\left({H, \circ_2}\right)$.

Then the operation $\circ$ in $\left({G \times T, \circ}\right)$ is associative.

Proof
By definition of group, both $\circ_1$ and $\circ_2$ are associative operations.

The result follows from External Direct Product Associativity, where the algebraic structures in question are groups.