Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-enq0 Unicode version

Definition df-enq0 7252
 Description: Define equivalence relation for nonnegative fractions. This is a "temporary" set used in the construction of complex numbers, and is intended to be used only by the construction. (Contributed by Jim Kingdon, 2-Nov-2019.)
Assertion
Ref Expression
df-enq0 ~Q0
Distinct variable group:   ,,,,,

Detailed syntax breakdown of Definition df-enq0
StepHypRef Expression
1 ceq0 7114 . 2 ~Q0
2 vx . . . . . . 7
32cv 1331 . . . . . 6
4 com 4508 . . . . . . 7
5 cnpi 7100 . . . . . . 7
64, 5cxp 4541 . . . . . 6
73, 6wcel 1481 . . . . 5
8 vy . . . . . . 7
98cv 1331 . . . . . 6
109, 6wcel 1481 . . . . 5
117, 10wa 103 . . . 4
12 vz . . . . . . . . . . . . 13
1312cv 1331 . . . . . . . . . . . 12
14 vw . . . . . . . . . . . . 13
1514cv 1331 . . . . . . . . . . . 12
1613, 15cop 3531 . . . . . . . . . . 11
173, 16wceq 1332 . . . . . . . . . 10
18 vv . . . . . . . . . . . . 13
1918cv 1331 . . . . . . . . . . . 12
20 vu . . . . . . . . . . . . 13
2120cv 1331 . . . . . . . . . . . 12
2219, 21cop 3531 . . . . . . . . . . 11
239, 22wceq 1332 . . . . . . . . . 10
2417, 23wa 103 . . . . . . . . 9
25 comu 6315 . . . . . . . . . . 11
2613, 21, 25co 5778 . . . . . . . . . 10
2715, 19, 25co 5778 . . . . . . . . . 10
2826, 27wceq 1332 . . . . . . . . 9
2924, 28wa 103 . . . . . . . 8
3029, 20wex 1469 . . . . . . 7
3130, 18wex 1469 . . . . . 6
3231, 14wex 1469 . . . . 5
3332, 12wex 1469 . . . 4
3411, 33wa 103 . . 3
3534, 2, 8copab 3992 . 2
361, 35wceq 1332 1 ~Q0
 Colors of variables: wff set class This definition is referenced by:  enq0enq  7259  enq0sym  7260  enq0ref  7261  enq0tr  7262  enq0er  7263  enq0breq  7264  enq0ex  7267
 Copyright terms: Public domain W3C validator