Subset of Set with Propositional Function

Theorem
Let $$S$$ be a set.

Let $$P: S \to \left\{{\text{true}, \text{false}}\right\}$$ be a propositional function on $$S$$.

Then
 * $$\left\{{x \in S: P \left({x}\right)} \right\} \subseteq S$$

Proof
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