Theorem refldcj

Description: The conjugation operation of the field of real numbers. (Contributed by Thierry Arnoux, 30-Jun-2019)

	Ref	Expression
Assertion	refldcj	$$⊢*={\mathrm{*}}_{{ℝ}_{\mathrm{fld}}}$$

Proof

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