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 ( π‘Š ∈ β„‚PreHil β†’ π‘Š ∈ NrmGrp )

Proof

Step Hyp Ref Expression
1 cphnlm ⊒ ( π‘Š ∈ β„‚PreHil β†’ π‘Š ∈ NrmMod )
2 nlmngp ⊒ ( π‘Š ∈ NrmMod β†’ π‘Š ∈ NrmGrp )
3 1 2 syl ⊒ ( π‘Š ∈ β„‚PreHil β†’ π‘Š ∈ NrmGrp )