MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-ltp Unicode version

Definition df-ltp 8609
Description: Define ordering on positive reals. This is a "temporary" set used in the construction of complex numbers df-c 8743, and is intended to be used only by the construction. From Proposition 9-3.2 of [Gleason] p. 122. (Contributed by NM, 14-Feb-1996.) (New usage is discouraged.)
Assertion
Ref Expression
df-ltp  |-  <P  =  { <. x ,  y
>.  |  ( (
x  e.  P.  /\  y  e.  P. )  /\  x  C.  y ) }
Distinct variable group:    x, y

Detailed syntax breakdown of Definition df-ltp
StepHypRef Expression
1 cltp 8485 . 2  class  <P
2 vx . . . . . . 7  set  x
32cv 1622 . . . . . 6  class  x
4 cnp 8481 . . . . . 6  class  P.
53, 4wcel 1684 . . . . 5  wff  x  e. 
P.
6 vy . . . . . . 7  set  y
76cv 1622 . . . . . 6  class  y
87, 4wcel 1684 . . . . 5  wff  y  e. 
P.
95, 8wa 358 . . . 4  wff  ( x  e.  P.  /\  y  e.  P. )
103, 7wpss 3153 . . . 4  wff  x  C.  y
119, 10wa 358 . . 3  wff  ( ( x  e.  P.  /\  y  e.  P. )  /\  x  C.  y )
1211, 2, 6copab 4076 . 2  class  { <. x ,  y >.  |  ( ( x  e.  P.  /\  y  e.  P. )  /\  x  C.  y ) }
131, 12wceq 1623 1  wff  <P  =  { <. x ,  y
>.  |  ( (
x  e.  P.  /\  y  e.  P. )  /\  x  C.  y ) }
Colors of variables: wff set class
This definition is referenced by:  ltrelpr  8622  ltprord  8654
  Copyright terms: Public domain W3C validator