Definition df-0r 7563

Description: Define signed real constant 0. 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-0r	⊢ 0R = [⟨1P, 1P⟩] ~R

Detailed syntax breakdown of Definition df-0r

Step	Hyp	Ref	Expression
1		c0r 7130	. 2 class 0R
2		c1p 7124	. . . 4 class 1P
3	2, 2	cop 3535	. . 3 class ⟨1P, 1P⟩
4		cer 7128	. . 3 class ~R
5	3, 4	cec 6435	. 2 class [⟨1P, 1P⟩] ~R
6	1, 5	wceq 1332	1 wff 0R = [⟨1P, 1P⟩] ~R

This definition is referenced by:  gt0srpr  7580  0r  7582  m1p1sr  7592  0lt1sr  7597  0idsr  7599  00sr  7601  suplocsrlempr  7639  pitoregt0  7681