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	$$⊢J\in \mathrm{TopOn}\left(B\right)$$
Assertion	toponunii	$$⊢B=\bigcup J$$

Proof

Step	Hyp	Ref	Expression
1		topontopi.1	$$⊢J\in \mathrm{TopOn}\left(B\right)$$
2		toponuni	$$⊢J\in \mathrm{TopOn}\left(B\right)\to B=\bigcup J$$
3	1 2	ax-mp	$$⊢B=\bigcup J$$