Theorem bj-rvecmod

Description: Real vector spaces are modules (elemental version). (Contributed by BJ, 6-Jan-2024)

	Ref	Expression
Assertion	bj-rvecmod	$$⊢V\in \mathrm{ℝVec}\to V\in \mathrm{LMod}$$

Proof

Step	Hyp	Ref	Expression
1		bj-isrvec	$$⊢V\in \mathrm{ℝVec}\leftrightarrow \left(V\in \mathrm{LMod}\wedge \mathrm{Scalar}\left(V\right)={ℝ}_{\mathrm{fld}}\right)$$
2	1	simplbi	$$⊢V\in \mathrm{ℝVec}\to V\in \mathrm{LMod}$$