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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