Set Equals Itself
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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 |
$\blacksquare$