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Mirrors > Home > ILE Home > Th. List > df-enq0 | Unicode version |
Description: Define equivalence relation for non-negative 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.) |
Ref | Expression |
---|---|
df-enq0 | ~Q0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ceq0 6384 | . 2 ~Q0 | |
2 | vx | . . . . . . 7 | |
3 | 2 | cv 1242 | . . . . . 6 |
4 | com 4313 | . . . . . . 7 | |
5 | cnpi 6370 | . . . . . . 7 | |
6 | 4, 5 | cxp 4343 | . . . . . 6 |
7 | 3, 6 | wcel 1393 | . . . . 5 |
8 | vy | . . . . . . 7 | |
9 | 8 | cv 1242 | . . . . . 6 |
10 | 9, 6 | wcel 1393 | . . . . 5 |
11 | 7, 10 | wa 97 | . . . 4 |
12 | vz | . . . . . . . . . . . . 13 | |
13 | 12 | cv 1242 | . . . . . . . . . . . 12 |
14 | vw | . . . . . . . . . . . . 13 | |
15 | 14 | cv 1242 | . . . . . . . . . . . 12 |
16 | 13, 15 | cop 3378 | . . . . . . . . . . 11 |
17 | 3, 16 | wceq 1243 | . . . . . . . . . 10 |
18 | vv | . . . . . . . . . . . . 13 | |
19 | 18 | cv 1242 | . . . . . . . . . . . 12 |
20 | vu | . . . . . . . . . . . . 13 | |
21 | 20 | cv 1242 | . . . . . . . . . . . 12 |
22 | 19, 21 | cop 3378 | . . . . . . . . . . 11 |
23 | 9, 22 | wceq 1243 | . . . . . . . . . 10 |
24 | 17, 23 | wa 97 | . . . . . . . . 9 |
25 | comu 5999 | . . . . . . . . . . 11 | |
26 | 13, 21, 25 | co 5512 | . . . . . . . . . 10 |
27 | 15, 19, 25 | co 5512 | . . . . . . . . . 10 |
28 | 26, 27 | wceq 1243 | . . . . . . . . 9 |
29 | 24, 28 | wa 97 | . . . . . . . 8 |
30 | 29, 20 | wex 1381 | . . . . . . 7 |
31 | 30, 18 | wex 1381 | . . . . . 6 |
32 | 31, 14 | wex 1381 | . . . . 5 |
33 | 32, 12 | wex 1381 | . . . 4 |
34 | 11, 33 | wa 97 | . . 3 |
35 | 34, 2, 8 | copab 3817 | . 2 |
36 | 1, 35 | wceq 1243 | 1 ~Q0 |
Colors of variables: wff set class |
This definition is referenced by: enq0enq 6529 enq0sym 6530 enq0ref 6531 enq0tr 6532 enq0er 6533 enq0breq 6534 enq0ex 6537 |
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