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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 24922. (Contributed by Scott Fenton, 3-Jun-2013.) |
Ref | Expression |
---|---|
df-btwn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbtwn 24912 |
. 2
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2 | vx |
. . . . . . . . 9
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3 | 2 | cv 1442 |
. . . . . . . 8
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4 | vn |
. . . . . . . . . 10
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5 | 4 | cv 1442 |
. . . . . . . . 9
![]() ![]() |
6 | cee 24911 |
. . . . . . . . 9
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7 | 5, 6 | cfv 5581 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() |
8 | 3, 7 | wcel 1886 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | vz |
. . . . . . . . 9
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10 | 9 | cv 1442 |
. . . . . . . 8
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11 | 10, 7 | wcel 1886 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | vy |
. . . . . . . . 9
![]() ![]() | |
13 | 12 | cv 1442 |
. . . . . . . 8
![]() ![]() |
14 | 13, 7 | wcel 1886 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 8, 11, 14 | w3a 984 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | vi |
. . . . . . . . . . 11
![]() ![]() | |
17 | 16 | cv 1442 |
. . . . . . . . . 10
![]() ![]() |
18 | 17, 13 | cfv 5581 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() |
19 | c1 9537 |
. . . . . . . . . . . 12
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20 | vt |
. . . . . . . . . . . . 13
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21 | 20 | cv 1442 |
. . . . . . . . . . . 12
![]() ![]() |
22 | cmin 9857 |
. . . . . . . . . . . 12
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23 | 19, 21, 22 | co 6288 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() |
24 | 17, 3 | cfv 5581 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() |
25 | cmul 9541 |
. . . . . . . . . . 11
![]() ![]() | |
26 | 23, 24, 25 | co 6288 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 17, 10 | cfv 5581 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() |
28 | 21, 27, 25 | co 6288 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
29 | caddc 9539 |
. . . . . . . . . 10
![]() ![]() | |
30 | 26, 28, 29 | co 6288 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | 18, 30 | wceq 1443 |
. . . . . . . 8
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32 | cfz 11781 |
. . . . . . . . 9
![]() ![]() | |
33 | 19, 5, 32 | co 6288 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() |
34 | 31, 16, 33 | wral 2736 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
35 | cc0 9536 |
. . . . . . . 8
![]() ![]() | |
36 | cicc 11635 |
. . . . . . . 8
![]() ![]() | |
37 | 35, 19, 36 | co 6288 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() |
38 | 34, 20, 37 | wrex 2737 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
39 | 15, 38 | wa 371 |
. . . . 5
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40 | cn 10606 |
. . . . 5
![]() ![]() | |
41 | 39, 4, 40 | wrex 2737 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
42 | 41, 2, 9, 12 | coprab 6289 |
. . 3
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43 | 42 | ccnv 4832 |
. 2
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44 | 1, 43 | wceq 1443 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: brbtwn 24922 |
Copyright terms: Public domain | W3C validator |