Definition df-1r 8093

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 7660	. 2 class 1R
2		c1p 7653	. . . . 5 class 1P
3		cpp 7654	. . . . 5 class +P
4	2, 2, 3	co 6079	. . . 4 class (1P +P 1P)
5	4, 2	cop 3711	. . 3 class ⟨(1P +P 1P), 1P⟩
6		cer 7657	. . 3 class ~R
7	5, 6	cec 6799	. 2 class [⟨(1P +P 1P), 1P⟩] ~R
8	1, 7	wceq 1402	1 wff 1R = [⟨(1P +P 1P), 1P⟩] ~R

This definition is referenced by:  1sr  8112  m1p1sr  8121  m1m1sr  8122  0lt1sr  8126  1idsr  8129  recexgt0sr  8134  caucvgsrlembound  8155  caucvgsr  8163  pitonnlem1  8206  pitonnlem2  8208  recidpirq  8219  nntopi  8255