Set is Element of its Power Set

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Theorem

A set is an element of its power set:

$S \in \powerset S$


Proof

\(\displaystyle \forall S: S\) \(\subseteq\) \(\displaystyle S\) Set is Subset of Itself
\(\displaystyle \leadsto \ \ \) \(\displaystyle \forall S: S\) \(\in\) \(\displaystyle \powerset S\) Definition of Power Set

$\blacksquare$


Also see


Sources