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Definition df-ltnqqs 6337
Description: Define ordering relation on positive fractions. This is a "temporary" set used in the construction of complex numbers, and is intended to be used only by the construction. Similar to Definition 5 of [Suppes] p. 162. (Contributed by NM, 13-Feb-1996.)
Assertion
Ref Expression
df-ltnqqs  <Q  { <. , 
>.  |  Q.  Q.  <. ,  >.  ~Q  <. ,  >.  ~Q  .N  <N  .N  }
Distinct variable group:   ,,,,,

Detailed syntax breakdown of Definition df-ltnqqs
StepHypRef Expression
1 cltq 6269 . 2  <Q
2 vx . . . . . . 7  setvar
32cv 1241 . . . . . 6
4 cnq 6264 . . . . . 6  Q.
53, 4wcel 1390 . . . . 5  Q.
6 vy . . . . . . 7  setvar
76cv 1241 . . . . . 6
87, 4wcel 1390 . . . . 5  Q.
95, 8wa 97 . . . 4  Q.  Q.
10 vz . . . . . . . . . . . . . 14  setvar
1110cv 1241 . . . . . . . . . . . . 13
12 vw . . . . . . . . . . . . . 14  setvar
1312cv 1241 . . . . . . . . . . . . 13
1411, 13cop 3370 . . . . . . . . . . . 12  <. ,  >.
15 ceq 6263 . . . . . . . . . . . 12  ~Q
1614, 15cec 6040 . . . . . . . . . . 11  <. ,  >.  ~Q
173, 16wceq 1242 . . . . . . . . . 10  <. ,  >.  ~Q
18 vv . . . . . . . . . . . . . 14  setvar
1918cv 1241 . . . . . . . . . . . . 13
20 vu . . . . . . . . . . . . . 14  setvar
2120cv 1241 . . . . . . . . . . . . 13
2219, 21cop 3370 . . . . . . . . . . . 12  <. ,  >.
2322, 15cec 6040 . . . . . . . . . . 11  <. ,  >.  ~Q
247, 23wceq 1242 . . . . . . . . . 10  <. ,  >.  ~Q
2517, 24wa 97 . . . . . . . . 9  <. ,  >.  ~Q  <. ,  >.  ~Q
26 cmi 6258 . . . . . . . . . . 11  .N
2711, 21, 26co 5455 . . . . . . . . . 10  .N
2813, 19, 26co 5455 . . . . . . . . . 10  .N
29 clti 6259 . . . . . . . . . 10  <N
3027, 28, 29wbr 3755 . . . . . . . . 9  .N  <N  .N
3125, 30wa 97 . . . . . . . 8  <. ,  >. 
~Q  <. ,  >.  ~Q  .N  <N  .N
3231, 20wex 1378 . . . . . . 7  <. ,  >. 
~Q  <. ,  >.  ~Q  .N  <N  .N
3332, 18wex 1378 . . . . . 6  <. ,  >.  ~Q  <. ,  >.  ~Q  .N  <N  .N
3433, 12wex 1378 . . . . 5  <. ,  >. 
~Q  <. ,  >.  ~Q  .N  <N  .N
3534, 10wex 1378 . . . 4  <. ,  >.  ~Q  <. ,  >.  ~Q  .N  <N  .N
369, 35wa 97 . . 3  Q.  Q.  <. ,  >. 
~Q  <. ,  >.  ~Q  .N  <N  .N
3736, 2, 6copab 3808 . 2  { <. ,  >.  |  Q.  Q.  <. ,  >. 
~Q  <. ,  >.  ~Q  .N  <N  .N  }
381, 37wceq 1242 1  <Q  { <. , 
>.  |  Q.  Q.  <. ,  >.  ~Q  <. ,  >.  ~Q  .N  <N  .N  }
Colors of variables: wff set class
This definition is referenced by:  ltrelnq  6349  ordpipqqs  6358
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