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Mirrors > Home > ILE Home > Th. List > df-enq | Unicode version |
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.) |
Ref | Expression |
---|---|
df-enq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ceq 7228 | . 2 | |
2 | vx | . . . . . . 7 | |
3 | 2 | cv 1347 | . . . . . 6 |
4 | cnpi 7221 | . . . . . . 7 | |
5 | 4, 4 | cxp 4607 | . . . . . 6 |
6 | 3, 5 | wcel 2141 | . . . . 5 |
7 | vy | . . . . . . 7 | |
8 | 7 | cv 1347 | . . . . . 6 |
9 | 8, 5 | wcel 2141 | . . . . 5 |
10 | 6, 9 | wa 103 | . . . 4 |
11 | vz | . . . . . . . . . . . . 13 | |
12 | 11 | cv 1347 | . . . . . . . . . . . 12 |
13 | vw | . . . . . . . . . . . . 13 | |
14 | 13 | cv 1347 | . . . . . . . . . . . 12 |
15 | 12, 14 | cop 3584 | . . . . . . . . . . 11 |
16 | 3, 15 | wceq 1348 | . . . . . . . . . 10 |
17 | vv | . . . . . . . . . . . . 13 | |
18 | 17 | cv 1347 | . . . . . . . . . . . 12 |
19 | vu | . . . . . . . . . . . . 13 | |
20 | 19 | cv 1347 | . . . . . . . . . . . 12 |
21 | 18, 20 | cop 3584 | . . . . . . . . . . 11 |
22 | 8, 21 | wceq 1348 | . . . . . . . . . 10 |
23 | 16, 22 | wa 103 | . . . . . . . . 9 |
24 | cmi 7223 | . . . . . . . . . . 11 | |
25 | 12, 20, 24 | co 5850 | . . . . . . . . . 10 |
26 | 14, 18, 24 | co 5850 | . . . . . . . . . 10 |
27 | 25, 26 | wceq 1348 | . . . . . . . . 9 |
28 | 23, 27 | wa 103 | . . . . . . . 8 |
29 | 28, 19 | wex 1485 | . . . . . . 7 |
30 | 29, 17 | wex 1485 | . . . . . 6 |
31 | 30, 13 | wex 1485 | . . . . 5 |
32 | 31, 11 | wex 1485 | . . . 4 |
33 | 10, 32 | wa 103 | . . 3 |
34 | 33, 2, 7 | copab 4047 | . 2 |
35 | 1, 34 | wceq 1348 | 1 |
Colors of variables: wff set class |
This definition is referenced by: enqbreq 7305 enqer 7307 enqex 7309 addpipqqs 7319 mulpipqqs 7322 enq0enq 7380 |
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