Metamath Proof Explorer

Theorem cphngp

Description: A subcomplex pre-Hilbert space is a normed group. (Contributed by Mario Carneiro, 13-Oct-2015)

Ref Expression
Assertion cphngp ⊢W∈CPreHil→W∈NrmGrp

Proof

Step Hyp Ref Expression
1 cphnlm ⊢W∈CPreHil→W∈NrmMod
2 nlmngp ⊢W∈NrmMod→W∈NrmGrp
3 1 2 syl ⊢W∈CPreHil→W∈NrmGrp