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 ) |
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 ) |