Definition df-1r 7673

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 7240	. 2 class 1R
2		c1p 7233	. . . . 5 class 1P
3		cpp 7234	. . . . 5 class +P.
4	2, 2, 3	co 5842	. . . 4 class ( 1P +P. 1P )
5	4, 2	cop 3579	. . 3 class <. ( 1P +P. 1P ) , 1P >.
6		cer 7237	. . 3 class ~R
7	5, 6	cec 6499	. 2 class [ <. ( 1P +P. 1P ) , 1P >. ] ~R
8	1, 7	wceq 1343	1 wff 1R = [ <. ( 1P +P. 1P ) , 1P >. ] ~R

This definition is referenced by:  1sr  7692  m1p1sr  7701  m1m1sr  7702  0lt1sr  7706  1idsr  7709  recexgt0sr  7714  caucvgsrlembound  7735  caucvgsr  7743  pitonnlem1  7786  pitonnlem2  7788  recidpirq  7799  nntopi  7835