MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-0r Structured version   Visualization version   GIF version

Definition df-0r 10167
Description: Define signed real constant 0. This is a "temporary" set used in the construction of complex numbers df-c 10227, 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.) (New usage is discouraged.)
Assertion
Ref Expression
df-0r 0R = [⟨1P, 1P⟩] ~R

Detailed syntax breakdown of Definition df-0r
StepHypRef Expression
1 c0r 9973 . 2 class 0R
2 c1p 9967 . . . 4 class 1P
32, 2cop 4376 . . 3 class ⟨1P, 1P
4 cer 9971 . . 3 class ~R
53, 4cec 7977 . 2 class [⟨1P, 1P⟩] ~R
61, 5wceq 1637 1 wff 0R = [⟨1P, 1P⟩] ~R
Colors of variables: wff setvar class
This definition is referenced by:  gt0srpr  10184  0r  10186  m1p1sr  10198  0lt1sr  10201  0idsr  10203  00sr  10205  supsrlem  10217
  Copyright terms: Public domain W3C validator