MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-1r Structured version   Visualization version   GIF version

Definition df-1r 10818
Description: Define signed real constant 1. This is a "temporary" set used in the construction of complex numbers df-c 10878, 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-1r 1R = [⟨(1P +P 1P), 1P⟩] ~R

Detailed syntax breakdown of Definition df-1r
StepHypRef Expression
1 c1r 10624 . 2 class 1R
2 c1p 10617 . . . . 5 class 1P
3 cpp 10618 . . . . 5 class +P
42, 2, 3co 7271 . . . 4 class (1P +P 1P)
54, 2cop 4573 . . 3 class ⟨(1P +P 1P), 1P
6 cer 10621 . . 3 class ~R
75, 6cec 8479 . 2 class [⟨(1P +P 1P), 1P⟩] ~R
81, 7wceq 1542 1 wff 1R = [⟨(1P +P 1P), 1P⟩] ~R
Colors of variables: wff setvar class
This definition is referenced by:  1sr  10838  m1p1sr  10849  m1m1sr  10850  0lt1sr  10852  1idsr  10855  recexsrlem  10860
  Copyright terms: Public domain W3C validator