Theorem rele2

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

	Ref	Expression
Assertion	rele2	$$⊢\le ={\le }_{{ℝ}_{\mathrm{fld}}}$$

Proof

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