Theorem lveclmod

Description: A left vector space is a left module. (Contributed by NM, 9-Dec-2013)

	Ref	Expression
Assertion	lveclmod	$$⊢W\in \mathrm{LVec}\to W\in \mathrm{LMod}$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢\mathrm{Scalar}\left(W\right)=\mathrm{Scalar}\left(W\right)$$
2	1	islvec	$$⊢W\in \mathrm{LVec}\leftrightarrow \left(W\in \mathrm{LMod}\wedge \mathrm{Scalar}\left(W\right)\in \mathrm{DivRing}\right)$$
3	2	simplbi	$$⊢W\in \mathrm{LVec}\to W\in \mathrm{LMod}$$