This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem ngptps

Description: A normed group is a topological space. (Contributed by Mario Carneiro, 5-Oct-2015)

		Ref	Expression
	Assertion	ngptps	$⊢ G \in NrmGrp \to G \in TopSp$

Step	Hyp	Ref	Expression
1		ngpms	$⊢ G \in NrmGrp \to G \in MetSp$
2		mstps	$⊢ G \in MetSp \to G \in TopSp$
3	1 2	syl	$⊢ G \in NrmGrp \to G \in TopSp$