Factor Spaces are T4 if Product Space is T4

Theorem
Let $\mathbb S = \family{\struct{S_\alpha, \tau_\alpha}}_{\alpha \mathop \in I}$ be an indexed family of topological spaces for $\alpha$ in some indexing set $I$.

Let $\displaystyle T = \struct{S, \tau} = \displaystyle \prod_{\alpha \mathop \in I} \struct{S_\alpha, \tau_\alpha}$ be the product space of $\mathbb S$.

Let $T$ be a $T_4$ space.

Then each of $\struct{S_\alpha, \tau_\alpha}$ is a $T_4$ space.