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 e. Ban -> W e. NrmGrp )

Proof

Step Hyp Ref Expression
1 bnnlm 
 |-  ( W e. Ban -> W e. NrmMod )
2 nlmngp 
 |-  ( W e. NrmMod -> W e. NrmGrp )
3 1 2 syl 
 |-  ( W e. Ban -> W e. NrmGrp )