Theorem toptopon2

Description: A topology is the same thing as a topology on the union of its open sets. (Contributed by BJ, 27-Apr-2021)

	Ref	Expression
Assertion	toptopon2	$$⊢J\in \mathrm{Top}\leftrightarrow J\in \mathrm{TopOn}\left(\bigcup J\right)$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢\bigcup J=\bigcup J$$
2	1	toptopon	$$⊢J\in \mathrm{Top}\leftrightarrow J\in \mathrm{TopOn}\left(\bigcup J\right)$$