Metamath Proof Explorer

Theorem bnngp

Description: A Banach space is a normed group. (Contributed by Mario Carneiro, 15-Oct-2015)

		Ref	Expression
	Assertion	bnngp	$⊢ W \in Ban \to W \in NrmGrp$

Step	Hyp	Ref	Expression
1		bnnlm	$⊢ W \in Ban \to W \in NrmMod$
2		nlmngp	$⊢ W \in NrmMod \to W \in NrmGrp$
3	1 2	syl	$⊢ W \in Ban \to W \in NrmGrp$