Subset of Set with Propositional Function

Theorem

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

In this context, $$P \left({x}\right)$$ is a propositional function which returns a value of true or false depending both on the value of $$x$$ and the nature of $$P$$.

Proof
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