Theorem remulr

Description: The multiplication operation of the field of reals. (Contributed by Thierry Arnoux, 1-Nov-2017)

	Ref	Expression
Assertion	remulr	$$⊢\times ={\cdot }_{{ℝ}_{\mathrm{fld}}}$$

Proof

Step	Hyp	Ref	Expression
1		reex	$$⊢ℝ\in \mathrm{V}$$
2		df-refld	$$⊢{ℝ}_{\mathrm{fld}}={ℂ}_{\mathrm{fld}}{\upharpoonright }_{𝑠}ℝ$$
3		cnfldmul	$$⊢\times ={\cdot }_{{ℂ}_{\mathrm{fld}}}$$
4	2 3	ressmulr	$$⊢ℝ\in \mathrm{V}\to \times ={\cdot }_{{ℝ}_{\mathrm{fld}}}$$
5	1 4	ax-mp	$$⊢\times ={\cdot }_{{ℝ}_{\mathrm{fld}}}$$