Definition df-1r 7564

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 7131	. 2 class 1R
2		c1p 7124	. . . . 5 class 1P
3		cpp 7125	. . . . 5 class +P.
4	2, 2, 3	co 5782	. . . 4 class ( 1P +P. 1P )
5	4, 2	cop 3535	. . 3 class <. ( 1P +P. 1P ) , 1P >.
6		cer 7128	. . 3 class ~R
7	5, 6	cec 6435	. 2 class [ <. ( 1P +P. 1P ) , 1P >. ] ~R
8	1, 7	wceq 1332	1 wff 1R = [ <. ( 1P +P. 1P ) , 1P >. ] ~R

This definition is referenced by:  1sr  7583  m1p1sr  7592  m1m1sr  7593  0lt1sr  7597  1idsr  7600  recexgt0sr  7605  caucvgsrlembound  7626  caucvgsr  7634  pitonnlem1  7677  pitonnlem2  7679  recidpirq  7690  nntopi  7726