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Metamath Proof Explorer

Theorem toponunii

Description: The base set of a topology on a given base set. (Contributed by Mario Carneiro, 13-Aug-2015)

		Ref	Expression
	Hypothesis	topontopi.1	$⊢ J \in TopOn (B)$
	Assertion	toponunii	$⊢ B = ⋃ J$

Step	Hyp	Ref	Expression
1		topontopi.1	$⊢ J \in TopOn (B)$
2		toponuni	$⊢ J \in TopOn (B) \to B = ⋃ J$
3	1 2	ax-mp	$⊢ B = ⋃ J$