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Metamath Proof Explorer

Definition df-1r

Description: Define signed real constant 1. 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, 9-Aug-1995) (New usage is discouraged.)

		Ref	Expression
	Assertion	df-1r	$⊢ 1_{𝑹} = [⟨1_{𝑷} +_{𝑷} 1_{𝑷}, 1_{𝑷}⟩] ~_{𝑹}$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		c1r	$class 1_{𝑹}$
1		c1p	$class 1_{𝑷}$
2		cpp	$class +_{𝑷}$
3	1 1 2	co	$class (1_{𝑷} +_{𝑷} 1_{𝑷})$
4	3 1	cop	$class ⟨1_{𝑷} +_{𝑷} 1_{𝑷}, 1_{𝑷}⟩$
5		cer	$class ~_{𝑹}$
6	4 5	cec	$class [⟨1_{𝑷} +_{𝑷} 1_{𝑷}, 1_{𝑷}⟩] ~_{𝑹}$
7	0 6	wceq	$wff 1_{𝑹} = [⟨1_{𝑷} +_{𝑷} 1_{𝑷}, 1_{𝑷}⟩] ~_{𝑹}$