Theorem regtop

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

	Ref	Expression
Assertion	regtop	$$⊢J\in \mathrm{Reg}\to J\in \mathrm{Top}$$

Proof

Step	Hyp	Ref	Expression
1		isreg	$$⊢J\in \mathrm{Reg}\leftrightarrow \left(J\in \mathrm{Top}\wedge \forall x\in J\forall y\in x\exists z\in J\left(y\in z\wedge \mathrm{cls}\left(J\right)\left(z\right)\subseteq x\right)\right)$$
2	1	simplbi	$$⊢J\in \mathrm{Reg}\to J\in \mathrm{Top}$$