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Metamath Proof Explorer

Theorem toponuni

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

		Ref	Expression
	Assertion	toponuni	$⊢ J \in TopOn (B) \to B = ⋃ J$

Step	Hyp	Ref	Expression
1		istopon	$⊢ J \in TopOn (B) \leftrightarrow (J \in Top \land B = ⋃ J)$
2	1	simprbi	$⊢ J \in TopOn (B) \to B = ⋃ J$