Definition df-1r 7799

Description: Define signed real constant 1. This is a "temporary" set used in the construction of complex numbers, 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.)

Assertion

Ref	Expression
df-1r	|- 1R = [ <. ( 1P +P. 1P ) , 1P >. ] ~R

Detailed syntax breakdown of Definition df-1r

Step	Hyp	Ref	Expression
1		c1r 7366	. 2 class 1R
2		c1p 7359	. . . . 5 class 1P
3		cpp 7360	. . . . 5 class +P.
4	2, 2, 3	co 5922	. . . 4 class ( 1P +P. 1P )
5	4, 2	cop 3625	. . 3 class <. ( 1P +P. 1P ) , 1P >.
6		cer 7363	. . 3 class ~R
7	5, 6	cec 6590	. 2 class [ <. ( 1P +P. 1P ) , 1P >. ] ~R
8	1, 7	wceq 1364	1 wff 1R = [ <. ( 1P +P. 1P ) , 1P >. ] ~R

This definition is referenced by:  1sr  7818  m1p1sr  7827  m1m1sr  7828  0lt1sr  7832  1idsr  7835  recexgt0sr  7840  caucvgsrlembound  7861  caucvgsr  7869  pitonnlem1  7912  pitonnlem2  7914  recidpirq  7925  nntopi  7961