Theorem t0top

Description: A T_0 space is a topological space. (Contributed by Jeff Hankins, 1-Feb-2010)

	Ref	Expression
Assertion	t0top	$$⊢J\in \mathrm{Kol2}\to J\in \mathrm{Top}$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢\bigcup J=\bigcup J$$
2	1	ist0	$$⊢J\in \mathrm{Kol2}\leftrightarrow \left(J\in \mathrm{Top}\wedge \forall x\in \bigcup J\forall y\in \bigcup J\left(\forall o\in J\left(x\in o\leftrightarrow y\in o\right)\to x=y\right)\right)$$
3	2	simplbi	$$⊢J\in \mathrm{Kol2}\to J\in \mathrm{Top}$$