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Metamath Proof Explorer

Theorem cphlmod

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

Ref Expression
Assertion cphlmod ⊢ W ∈ CPreHil → W ∈ LMod

Proof

Step Hyp Ref Expression
1 cphnlm ⊢ W ∈ CPreHil → W ∈ NrmMod
2 nlmlmod ⊢ W ∈ NrmMod → W ∈ LMod
3 1 2 syl ⊢ W ∈ CPreHil → W ∈ LMod