Theorem replusg

Description: The addition operation of the field of reals. (Contributed by Thierry Arnoux, 21-Jan-2018)

	Ref	Expression
Assertion	replusg	$$⊢+={+}_{{ℝ}_{\mathrm{fld}}}$$

Proof

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