Partition Topology is T5

Theorem
Let $S$ be a set and let $\mathcal P$ be a partition on $S$ which is not the (trivial) partition of singletons.

Let $T = \left({S, \vartheta}\right)$ be the partition space whose basis is $\mathcal P$.

Then $T$ is a $T_5$ space.

Thus $T$ is also a $T_4$ space.