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Metamath Proof Explorer

Theorem replusg

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

		Ref	Expression
	Assertion	replusg	$⊢ + = +_{ℝ_{fld}}$

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