Metamath Proof Explorer

Theorem cphlvec

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

Ref Expression
Assertion cphlvec 
|- ( W e. CPreHil -> W e. LVec )

Proof

Step Hyp Ref Expression
1 cphphl 
 |-  ( W e. CPreHil -> W e. PreHil )
2 phllvec 
 |-  ( W e. PreHil -> W e. LVec )
3 1 2 syl 
 |-  ( W e. CPreHil -> W e. LVec )