Theorem bj-rvecrr

Description: The field of scalars of a real vector space is the field of real numbers. (Contributed by BJ, 6-Jan-2024)

	Ref	Expression
Assertion	bj-rvecrr	$$⊢V\in \mathrm{ℝVec}\to \mathrm{Scalar}\left(V\right)={ℝ}_{\mathrm{fld}}$$

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	simprbi	$$⊢V\in \mathrm{ℝVec}\to \mathrm{Scalar}\left(V\right)={ℝ}_{\mathrm{fld}}$$