Theorem phllmod

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

	Ref	Expression
Assertion	phllmod	$$⊢W\in \mathrm{PreHil}\to W\in \mathrm{LMod}$$

Proof

Step	Hyp	Ref	Expression
1		phllvec	$$⊢W\in \mathrm{PreHil}\to W\in \mathrm{LVec}$$
2		lveclmod	$$⊢W\in \mathrm{LVec}\to W\in \mathrm{LMod}$$
3	1 2	syl	$$⊢W\in \mathrm{PreHil}\to W\in \mathrm{LMod}$$