Theorem nrmtop

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

	Ref	Expression
Assertion	nrmtop	$$⊢J\in \mathrm{Nrm}\to J\in \mathrm{Top}$$

Proof

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