Theorem rebase

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

	Ref	Expression
Assertion	rebase	$$⊢ℝ={\mathrm{Base}}_{{ℝ}_{\mathrm{fld}}}$$

Proof

Step	Hyp	Ref	Expression
1		ax-resscn	$$⊢ℝ\subseteq ℂ$$
2		df-refld	$$⊢{ℝ}_{\mathrm{fld}}={ℂ}_{\mathrm{fld}}{\upharpoonright }_{𝑠}ℝ$$
3		cnfldbas	$$⊢ℂ={\mathrm{Base}}_{{ℂ}_{\mathrm{fld}}}$$
4	2 3	ressbas2	$$⊢ℝ\subseteq ℂ\to ℝ={\mathrm{Base}}_{{ℝ}_{\mathrm{fld}}}$$
5	1 4	ax-mp	$$⊢ℝ={\mathrm{Base}}_{{ℝ}_{\mathrm{fld}}}$$