Partition of Singletons yields Discrete Topology

Theorem
Let $S$ be a set which is non-empty.

Let $\mathcal P$ be the (trivial) partition of singletons on $S$:
 * $\mathcal P = \left\{{\left\{{x}\right\}: x \in S}\right\}$

Then the partition topology on $\mathcal P$ is the discrete topology.

Proof
From Basis for Discrete Topology it is shown that $\mathcal P$ as defined here forms the basis of the discrete topology.