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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 × P ) / ~_R )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cnr	⊢ R
1		cnp	⊢ P
2	1 1	cxp	⊢ ( P × P )
3		cer	⊢ ~_R
4	2 3	cqs	⊢ ( ( P × P ) / ~_R )
5	0 4	wceq	⊢ R = ( ( P × P ) / ~_R )