Intersection is Subset

Theorem
The intersection of two sets is a subset of each:


 * $$S \cap T \subseteq S$$
 * $$S \cap T \subseteq T$$

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:
 * $$\forall T \in \mathbb S: \bigcap \mathbb S \subseteq T$$

Proof
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Similarly for $$T$$.

Proof of General Result
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