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 )