Theorem nvclmod

Description: A normed vector space is a left module. (Contributed by Mario Carneiro, 4-Oct-2015)

	Ref	Expression
Assertion	nvclmod	$$⊢W\in \mathrm{NrmVec}\to W\in \mathrm{LMod}$$

Proof

Step	Hyp	Ref	Expression
1		nvcnlm	$$⊢W\in \mathrm{NrmVec}\to W\in \mathrm{NrmMod}$$
2		nlmlmod	$$⊢W\in \mathrm{NrmMod}\to W\in \mathrm{LMod}$$
3	1 2	syl	$$⊢W\in \mathrm{NrmVec}\to W\in \mathrm{LMod}$$