Theorem bj-vecssmod

Description: Vector spaces are modules. (Contributed by BJ, 9-Jun-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-vecssmod	$$⊢\mathrm{LVec}\subseteq \mathrm{LMod}$$

Proof

Step	Hyp	Ref	Expression
1		df-lvec	$$⊢\mathrm{LVec}=\left\{x\in \mathrm{LMod}|\mathrm{Scalar}\left(x\right)\in \mathrm{DivRing}\right\}$$
2		ssrab2	$$⊢\left\{x\in \mathrm{LMod}|\mathrm{Scalar}\left(x\right)\in \mathrm{DivRing}\right\}\subseteq \mathrm{LMod}$$
3	1 2	eqsstri	$$⊢\mathrm{LVec}\subseteq \mathrm{LMod}$$