Metamath Proof Explorer

Theorem cphlmod

Description: A subcomplex pre-Hilbert space is a left module. (Contributed by Mario Carneiro, 7-Oct-2015)

Ref Expression
Assertion cphlmod ⊢W∈CPreHil→W∈LMod

Proof

Step Hyp Ref Expression
1 cphnlm ⊢W∈CPreHil→W∈NrmMod
2 nlmlmod ⊢W∈NrmMod→W∈LMod
3 1 2 syl ⊢W∈CPreHil→W∈LMod