Metamath Proof Explorer

Theorem ngpxms

Description: A normed group is an extended metric space. (Contributed by Mario Carneiro, 2-Oct-2015)

		Ref	Expression
	Assertion	ngpxms	$⊢ G \in NrmGrp \to G \in ∞MetSp$

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