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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 )

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