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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-bnj18 | Structured version Visualization version Unicode version |
Description: Define the function
giving: the transitive closure of ![]() ![]() ![]() |
Ref | Expression |
---|---|
df-bnj18 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . 3
![]() ![]() | |
2 | cR |
. . 3
![]() ![]() | |
3 | cX |
. . 3
![]() ![]() | |
4 | 1, 2, 3 | c-bnj18 29511 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | vf |
. . 3
![]() ![]() | |
6 | 5 | cv 1445 |
. . . . . . 7
![]() ![]() |
7 | vn |
. . . . . . . 8
![]() ![]() | |
8 | 7 | cv 1445 |
. . . . . . 7
![]() ![]() |
9 | 6, 8 | wfn 5580 |
. . . . . 6
![]() ![]() ![]() ![]() |
10 | c0 3733 |
. . . . . . . 8
![]() ![]() | |
11 | 10, 6 | cfv 5585 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() |
12 | 1, 2, 3 | c-bnj14 29505 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | 11, 12 | wceq 1446 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | vi |
. . . . . . . . . . 11
![]() ![]() | |
15 | 14 | cv 1445 |
. . . . . . . . . 10
![]() ![]() |
16 | 15 | csuc 5428 |
. . . . . . . . 9
![]() ![]() ![]() |
17 | 16, 8 | wcel 1889 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() |
18 | 16, 6 | cfv 5585 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | vy |
. . . . . . . . . 10
![]() ![]() | |
20 | 15, 6 | cfv 5585 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() |
21 | 19 | cv 1445 |
. . . . . . . . . . 11
![]() ![]() |
22 | 1, 2, 21 | c-bnj14 29505 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 19, 20, 22 | ciun 4281 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 18, 23 | wceq 1446 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 17, 24 | wi 4 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | com 6697 |
. . . . . . 7
![]() ![]() | |
27 | 25, 14, 26 | wral 2739 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | 9, 13, 27 | w3a 986 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
29 | 10 | csn 3970 |
. . . . . 6
![]() ![]() ![]() ![]() |
30 | 26, 29 | cdif 3403 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | 28, 7, 30 | wrex 2740 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 31, 5 | cab 2439 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
33 | 6 | cdm 4837 |
. . . 4
![]() ![]() ![]() |
34 | 14, 33, 20 | ciun 4281 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
35 | 5, 32, 34 | ciun 4281 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
36 | 4, 35 | wceq 1446 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
This definition is referenced by: bnj882 29749 bnj18eq1 29750 |
Copyright terms: Public domain | W3C validator |