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 )