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Mirrors > Home > MPE Home > Th. List > df-btwn | Structured version Visualization version Unicode version |
Description: Define the Euclidean betweenness predicate. For details, see brbtwn 25779. (Contributed by Scott Fenton, 3-Jun-2013.) |
Ref | Expression |
---|---|
df-btwn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbtwn 25769 | . 2 | |
2 | vx | . . . . . . . . 9 | |
3 | 2 | cv 1482 | . . . . . . . 8 |
4 | vn | . . . . . . . . . 10 | |
5 | 4 | cv 1482 | . . . . . . . . 9 |
6 | cee 25768 | . . . . . . . . 9 | |
7 | 5, 6 | cfv 5888 | . . . . . . . 8 |
8 | 3, 7 | wcel 1990 | . . . . . . 7 |
9 | vz | . . . . . . . . 9 | |
10 | 9 | cv 1482 | . . . . . . . 8 |
11 | 10, 7 | wcel 1990 | . . . . . . 7 |
12 | vy | . . . . . . . . 9 | |
13 | 12 | cv 1482 | . . . . . . . 8 |
14 | 13, 7 | wcel 1990 | . . . . . . 7 |
15 | 8, 11, 14 | w3a 1037 | . . . . . 6 |
16 | vi | . . . . . . . . . . 11 | |
17 | 16 | cv 1482 | . . . . . . . . . 10 |
18 | 17, 13 | cfv 5888 | . . . . . . . . 9 |
19 | c1 9937 | . . . . . . . . . . . 12 | |
20 | vt | . . . . . . . . . . . . 13 | |
21 | 20 | cv 1482 | . . . . . . . . . . . 12 |
22 | cmin 10266 | . . . . . . . . . . . 12 | |
23 | 19, 21, 22 | co 6650 | . . . . . . . . . . 11 |
24 | 17, 3 | cfv 5888 | . . . . . . . . . . 11 |
25 | cmul 9941 | . . . . . . . . . . 11 | |
26 | 23, 24, 25 | co 6650 | . . . . . . . . . 10 |
27 | 17, 10 | cfv 5888 | . . . . . . . . . . 11 |
28 | 21, 27, 25 | co 6650 | . . . . . . . . . 10 |
29 | caddc 9939 | . . . . . . . . . 10 | |
30 | 26, 28, 29 | co 6650 | . . . . . . . . 9 |
31 | 18, 30 | wceq 1483 | . . . . . . . 8 |
32 | cfz 12326 | . . . . . . . . 9 | |
33 | 19, 5, 32 | co 6650 | . . . . . . . 8 |
34 | 31, 16, 33 | wral 2912 | . . . . . . 7 |
35 | cc0 9936 | . . . . . . . 8 | |
36 | cicc 12178 | . . . . . . . 8 | |
37 | 35, 19, 36 | co 6650 | . . . . . . 7 |
38 | 34, 20, 37 | wrex 2913 | . . . . . 6 |
39 | 15, 38 | wa 384 | . . . . 5 |
40 | cn 11020 | . . . . 5 | |
41 | 39, 4, 40 | wrex 2913 | . . . 4 |
42 | 41, 2, 9, 12 | coprab 6651 | . . 3 |
43 | 42 | ccnv 5113 | . 2 |
44 | 1, 43 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: brbtwn 25779 |
Copyright terms: Public domain | W3C validator |