Binary Cartesian Product in Kuratowski Formalization contained in Power Set of Power Set of Union

Theorem
Let $S$ and $T$ be sets.

Let $S \times T$ be the Cartesian product of $S$ and $T$ realized as a set of ordered pairs in Kuratowski formalization.

Then $S \times T \subseteq \powerset {\powerset {S \cup T} }$.