Metamath Proof Explorer

Theorem phllmod

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

Ref Expression
Assertion phllmod 
|- ( W e. PreHil -> W e. LMod )

Proof

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