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Metamath Proof Explorer

Definition df-nr

Description: Define class of signed reals. This is a "temporary" set used in the construction of complex numbers df-c , and is intended to be used only by the construction. From Proposition 9-4.2 of Gleason p. 126. (Contributed by NM, 25-Jul-1995) (New usage is discouraged.)

		Ref	Expression
	Assertion	df-nr	$⊢ 𝑹 = (𝑷 \times 𝑷) / ~_{𝑹}$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cnr	$class 𝑹$
1		cnp	$class 𝑷$
2	1 1	cxp	$class (𝑷 \times 𝑷)$
3		cer	$class ~_{𝑹}$
4	2 3	cqs	$class ((𝑷 \times 𝑷) / ~_{𝑹})$
5	0 4	wceq	$wff 𝑹 = (𝑷 \times 𝑷) / ~_{𝑹}$