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Metamath Proof Explorer

Theorem pnrmtop

Description: A perfectly normal space is a topological space. (Contributed by Mario Carneiro, 26-Aug-2015)

		Ref	Expression
	Assertion	pnrmtop	$⊢ J \in PNrm \to J \in Top$

Step	Hyp	Ref	Expression
1		pnrmnrm	$⊢ J \in PNrm \to J \in Nrm$
2		nrmtop	$⊢ J \in Nrm \to J \in Top$
3	1 2	syl	$⊢ J \in PNrm \to J \in Top$