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 ∈ PreHil → W ∈ LMod

Proof

Step Hyp Ref Expression
1 phllvec ⊢ W ∈ PreHil → W ∈ LVec
2 lveclmod ⊢ W ∈ LVec → W ∈ LMod
3 1 2 syl ⊢ W ∈ PreHil → W ∈ LMod