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 e. CPreHil -> W e. LMod )

Proof

Step Hyp Ref Expression
1 cphnlm 
 |-  ( W e. CPreHil -> W e. NrmMod )
2 nlmlmod 
 |-  ( W e. NrmMod -> W e. LMod )
3 1 2 syl 
 |-  ( W e. CPreHil -> W e. LMod )