Theorem topontop

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

	Ref	Expression
Assertion	topontop	$$⊢J\in \mathrm{TopOn}\left(B\right)\to J\in \mathrm{Top}$$

Proof

Step	Hyp	Ref	Expression
1		istopon	$$⊢J\in \mathrm{TopOn}\left(B\right)\leftrightarrow \left(J\in \mathrm{Top}\wedge B=\bigcup J\right)$$
2	1	simplbi	$$⊢J\in \mathrm{TopOn}\left(B\right)\to J\in \mathrm{Top}$$