Normal Subgroups that Intersect Trivially

Proposition

Let $H$ and $K$ be normal subgroups of a group $G$ such that they intersect trivially. Then $hk=kh$ for any $h\in H$ and $k\in K$.

\begin{proof} Note that $hk{h}^{-1}{k}^{-1}\in H\cap K=\{1\}$. \end{proof}