Theorem t1top

Description: A T_1 space is a topological space. (Contributed by Jeff Hankins, 1-Feb-2010)

	Ref	Expression
Assertion	t1top	$$⊢J\in \mathrm{Fre}\to J\in \mathrm{Top}$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢\bigcup J=\bigcup J$$
2	1	ist1	$$⊢J\in \mathrm{Fre}\leftrightarrow \left(J\in \mathrm{Top}\wedge \forall x\in \bigcup J\left\{x\right\}\in \mathrm{Clsd}\left(J\right)\right)$$
3	2	simplbi	$$⊢J\in \mathrm{Fre}\to J\in \mathrm{Top}$$