Set Equals Itself

Theorem

All sets are equal to themselves:

$\forall S: S = S$


Proof

\(\ds S \subseteq S\) \(=\) \(\ds S \supseteq S\) Set is Subset of Itself
\(\ds \leadsto \ \ \) \(\ds S\) \(=\) \(\ds S\) Definition of Set Equality

$\blacksquare$

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