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Mirrors > Home > ILE Home > Th. List > vtocl3gaf | Unicode version |
Description: Implicit substitution of 3 classes for 3 setvar variables. (Contributed by NM, 10-Aug-2013.) (Revised by Mario Carneiro, 11-Oct-2016.) |
Ref | Expression |
---|---|
vtocl3gaf.a |
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vtocl3gaf.b |
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vtocl3gaf.c |
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vtocl3gaf.d |
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vtocl3gaf.e |
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vtocl3gaf.f |
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vtocl3gaf.1 |
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vtocl3gaf.2 |
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vtocl3gaf.3 |
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vtocl3gaf.4 |
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vtocl3gaf.5 |
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vtocl3gaf.6 |
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vtocl3gaf.7 |
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Ref | Expression |
---|---|
vtocl3gaf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtocl3gaf.a |
. . 3
![]() ![]() ![]() ![]() | |
2 | vtocl3gaf.b |
. . 3
![]() ![]() ![]() ![]() | |
3 | vtocl3gaf.c |
. . 3
![]() ![]() ![]() ![]() | |
4 | vtocl3gaf.d |
. . 3
![]() ![]() ![]() ![]() | |
5 | vtocl3gaf.e |
. . 3
![]() ![]() ![]() ![]() | |
6 | vtocl3gaf.f |
. . 3
![]() ![]() ![]() ![]() | |
7 | 1 | nfel1 2340 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
8 | nfv 1538 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() | |
9 | nfv 1538 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 7, 8, 9 | nf3an 1576 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | vtocl3gaf.1 |
. . . 4
![]() ![]() ![]() ![]() | |
12 | 10, 11 | nfim 1582 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | 2 | nfel1 2340 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
14 | 4 | nfel1 2340 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
15 | nfv 1538 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() | |
16 | 13, 14, 15 | nf3an 1576 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | vtocl3gaf.2 |
. . . 4
![]() ![]() ![]() ![]() | |
18 | 16, 17 | nfim 1582 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 3 | nfel1 2340 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
20 | 5 | nfel1 2340 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
21 | 6 | nfel1 2340 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
22 | 19, 20, 21 | nf3an 1576 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | vtocl3gaf.3 |
. . . 4
![]() ![]() ![]() ![]() | |
24 | 22, 23 | nfim 1582 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | eleq1 2250 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
26 | 25 | 3anbi1d 1326 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | vtocl3gaf.4 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
28 | 26, 27 | imbi12d 234 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
29 | eleq1 2250 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
30 | 29 | 3anbi2d 1327 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | vtocl3gaf.5 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
32 | 30, 31 | imbi12d 234 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
33 | eleq1 2250 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
34 | 33 | 3anbi3d 1328 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
35 | vtocl3gaf.6 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
36 | 34, 35 | imbi12d 234 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
37 | vtocl3gaf.7 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
38 | 1, 2, 3, 4, 5, 6, 12, 18, 24, 28, 32, 36, 37 | vtocl3gf 2812 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
39 | 38 | pm2.43i 49 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-v 2751 |
This theorem is referenced by: vtocl3ga 2819 |
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