Union of Subsets is Subset/Proof 1

Theorem
Let $S_1$, $S_2$, and $T$ be sets.

Suppose that $S_1$ and $S_2$ are both subsets of $T$.

Then:
 * $S_1 \cup S_2 \subseteq T$

That is:
 * $\left({S_1 \subseteq T}\right) \land \left({S_2 \subseteq T}\right) \implies \left({S_1 \cup S_2}\right) \subseteq T$

Proof
Let:
 * $\left({S_1 \subseteq T}\right) \land \left({S_2 \subseteq T}\right)$

Then: