Theorem topontopi

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

	Ref	Expression
Hypothesis	topontopi.1	⊢ 𝐽 ∈ ( TopOn ‘ 𝐵 )
Assertion	topontopi	⊢ 𝐽 ∈ Top

Proof

Step	Hyp	Ref	Expression
1		topontopi.1	⊢ 𝐽 ∈ ( TopOn ‘ 𝐵 )
2		topontop	⊢ ( 𝐽 ∈ ( TopOn ‘ 𝐵 ) → 𝐽 ∈ Top )
3	1 2	ax-mp	⊢ 𝐽 ∈ Top