ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-enq Structured version   Unicode version

Definition df-enq 6331
Description: Define equivalence relation for positive fractions. This is a "temporary" set used in the construction of complex numbers, and is intended to be used only by the construction. From Proposition 9-2.1 of [Gleason] p. 117. (Contributed by NM, 27-Aug-1995.)
Assertion
Ref Expression
df-enq  ~Q  { <. , 
>.  |  N.  X.  N.  N.  X.  N. 
<. ,  >.  <. ,  >.  .N  .N  }
Distinct variable group:   ,,,,,

Detailed syntax breakdown of Definition df-enq
StepHypRef Expression
1 ceq 6263 . 2  ~Q
2 vx . . . . . . 7  setvar
32cv 1241 . . . . . 6
4 cnpi 6256 . . . . . . 7  N.
54, 4cxp 4286 . . . . . 6  N. 
X.  N.
63, 5wcel 1390 . . . . 5  N.  X.  N.
7 vy . . . . . . 7  setvar
87cv 1241 . . . . . 6
98, 5wcel 1390 . . . . 5  N.  X.  N.
106, 9wa 97 . . . 4  N.  X.  N.  N.  X.  N.
11 vz . . . . . . . . . . . . 13  setvar
1211cv 1241 . . . . . . . . . . . 12
13 vw . . . . . . . . . . . . 13  setvar
1413cv 1241 . . . . . . . . . . . 12
1512, 14cop 3370 . . . . . . . . . . 11  <. ,  >.
163, 15wceq 1242 . . . . . . . . . 10  <. ,  >.
17 vv . . . . . . . . . . . . 13  setvar
1817cv 1241 . . . . . . . . . . . 12
19 vu . . . . . . . . . . . . 13  setvar
2019cv 1241 . . . . . . . . . . . 12
2118, 20cop 3370 . . . . . . . . . . 11  <. ,  >.
228, 21wceq 1242 . . . . . . . . . 10  <. ,  >.
2316, 22wa 97 . . . . . . . . 9  <. ,  >.  <. ,  >.
24 cmi 6258 . . . . . . . . . . 11  .N
2512, 20, 24co 5455 . . . . . . . . . 10  .N
2614, 18, 24co 5455 . . . . . . . . . 10  .N
2725, 26wceq 1242 . . . . . . . . 9  .N  .N
2823, 27wa 97 . . . . . . . 8  <. ,  >.  <. ,  >.  .N  .N
2928, 19wex 1378 . . . . . . 7  <. ,  >.  <. ,  >.  .N  .N
3029, 17wex 1378 . . . . . 6  <. ,  >.  <. ,  >.  .N  .N
3130, 13wex 1378 . . . . 5  <. ,  >.  <. ,  >.  .N  .N
3231, 11wex 1378 . . . 4 
<. ,  >.  <. ,  >.  .N  .N
3310, 32wa 97 . . 3  N.  X.  N.  N.  X.  N.  <. ,  >.  <. ,  >.  .N  .N
3433, 2, 7copab 3808 . 2  { <. ,  >.  |  N.  X.  N.  N.  X.  N.  <. ,  >.  <. ,  >.  .N  .N  }
351, 34wceq 1242 1  ~Q  { <. , 
>.  |  N.  X.  N.  N.  X.  N. 
<. ,  >.  <. ,  >.  .N  .N  }
Colors of variables: wff set class
This definition is referenced by:  enqbreq  6340  enqer  6342  enqex  6344  addpipqqs  6354  mulpipqqs  6357  enq0enq  6414
  Copyright terms: Public domain W3C validator