Set is Subset of Union

Theorem
The union of two sets is a superset of each:


 * $S \subseteq S \cup T$
 * $T \subseteq S \cup T$

General Result
Let $S$ be a set.

Let $\mathcal P \left({S}\right)$ be the power set of $S$.

Let $\mathbb S \subseteq \mathcal P \left({S}\right)$.

Then:
 * $\forall T \in \mathbb S: T \subseteq \bigcup \mathbb S$

Proof
Similarly for $T$.