Product Space is T3 1/2 iff Factor Spaces are T3 1/2

Theorem
Let $\mathbb S = \left\{{\left({S_\alpha, \tau_\alpha}\right)}\right\}$ be a set of topological spaces for $\alpha$ in some indexing set $I$ with $S_\alpha \neq \varnothing$ for every $\alpha \in I$.

Let $\displaystyle T = \left({S, \tau}\right) = \prod \left({S_\alpha, \tau_\alpha}\right)$ be the product space of $\mathbb S$.

Then $T$ is a $T_{3 \frac 1 2}$ space iff each of $\left({S_\alpha, \tau_\alpha}\right)$ is a $T_{3 \frac 1 2}$ space.