Definition df-1r 8099

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 7666	. 2 class 1R
2		c1p 7659	. . . . 5 class 1P
3		cpp 7660	. . . . 5 class +P.
4	2, 2, 3	co 6085	. . . 4 class ( 1P +P. 1P )
5	4, 2	cop 3712	. . 3 class <. ( 1P +P. 1P ) , 1P >.
6		cer 7663	. . 3 class ~R
7	5, 6	cec 6805	. 2 class [ <. ( 1P +P. 1P ) , 1P >. ] ~R
8	1, 7	wceq 1402	1 wff 1R = [ <. ( 1P +P. 1P ) , 1P >. ] ~R

This definition is used by:  1sr  8118  m1p1sr  8127  m1m1sr  8128  0lt1sr  8132  1idsr  8135  recexgt0sr  8140  caucvgsrlembound  8161  caucvgsr  8169  pitonnlem1  8212  pitonnlem2  8214  recidpirq  8225  nntopi  8261