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 ∈ Ban → W ∈ NrmGrp

Proof

Step Hyp Ref Expression
1 bnnlm ⊢ W ∈ Ban → W ∈ NrmMod
2 nlmngp ⊢ W ∈ NrmMod → W ∈ NrmGrp
3 1 2 syl ⊢ W ∈ Ban → W ∈ NrmGrp