Definition df-1r 7995

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 7562	. 2 class 1R
2		c1p 7555	. . . . 5 class 1P
3		cpp 7556	. . . . 5 class +P.
4	2, 2, 3	co 6028	. . . 4 class ( 1P +P. 1P )
5	4, 2	cop 3676	. . 3 class <. ( 1P +P. 1P ) , 1P >.
6		cer 7559	. . 3 class ~R
7	5, 6	cec 6743	. 2 class [ <. ( 1P +P. 1P ) , 1P >. ] ~R
8	1, 7	wceq 1398	1 wff 1R = [ <. ( 1P +P. 1P ) , 1P >. ] ~R

This definition is referenced by:  1sr  8014  m1p1sr  8023  m1m1sr  8024  0lt1sr  8028  1idsr  8031  recexgt0sr  8036  caucvgsrlembound  8057  caucvgsr  8065  pitonnlem1  8108  pitonnlem2  8110  recidpirq  8121  nntopi  8157