Description: A pre-Hilbert space is a left module. (Contributed by Mario Carneiro, 7-Oct-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | phllmod | ⊢ ( 𝑊 ∈ PreHil → 𝑊 ∈ LMod ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | phllvec | ⊢ ( 𝑊 ∈ PreHil → 𝑊 ∈ LVec ) | |
2 | lveclmod | ⊢ ( 𝑊 ∈ LVec → 𝑊 ∈ LMod ) | |
3 | 1 2 | syl | ⊢ ( 𝑊 ∈ PreHil → 𝑊 ∈ LMod ) |