Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 | |
vtocl3gaf.b | |
vtocl3gaf.c | |
vtocl3gaf.d | |
vtocl3gaf.e | |
vtocl3gaf.f | |
vtocl3gaf.1 | |
vtocl3gaf.2 | |
vtocl3gaf.3 | |
vtocl3gaf.4 | |
vtocl3gaf.5 | |
vtocl3gaf.6 | |
vtocl3gaf.7 |
Ref | Expression |
---|---|
vtocl3gaf |
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 2188 | . . . . 5 |
8 | nfv 1421 | . . . . 5 | |
9 | nfv 1421 | . . . . 5 | |
10 | 7, 8, 9 | nf3an 1458 | . . . 4 |
11 | vtocl3gaf.1 | . . . 4 | |
12 | 10, 11 | nfim 1464 | . . 3 |
13 | 2 | nfel1 2188 | . . . . 5 |
14 | 4 | nfel1 2188 | . . . . 5 |
15 | nfv 1421 | . . . . 5 | |
16 | 13, 14, 15 | nf3an 1458 | . . . 4 |
17 | vtocl3gaf.2 | . . . 4 | |
18 | 16, 17 | nfim 1464 | . . 3 |
19 | 3 | nfel1 2188 | . . . . 5 |
20 | 5 | nfel1 2188 | . . . . 5 |
21 | 6 | nfel1 2188 | . . . . 5 |
22 | 19, 20, 21 | nf3an 1458 | . . . 4 |
23 | vtocl3gaf.3 | . . . 4 | |
24 | 22, 23 | nfim 1464 | . . 3 |
25 | eleq1 2100 | . . . . 5 | |
26 | 25 | 3anbi1d 1211 | . . . 4 |
27 | vtocl3gaf.4 | . . . 4 | |
28 | 26, 27 | imbi12d 223 | . . 3 |
29 | eleq1 2100 | . . . . 5 | |
30 | 29 | 3anbi2d 1212 | . . . 4 |
31 | vtocl3gaf.5 | . . . 4 | |
32 | 30, 31 | imbi12d 223 | . . 3 |
33 | eleq1 2100 | . . . . 5 | |
34 | 33 | 3anbi3d 1213 | . . . 4 |
35 | vtocl3gaf.6 | . . . 4 | |
36 | 34, 35 | imbi12d 223 | . . 3 |
37 | vtocl3gaf.7 | . . 3 | |
38 | 1, 2, 3, 4, 5, 6, 12, 18, 24, 28, 32, 36, 37 | vtocl3gf 2616 | . 2 |
39 | 38 | pm2.43i 43 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 w3a 885 wceq 1243 wnf 1349 wcel 1393 wnfc 2165 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 |
This theorem is referenced by: vtocl3ga 2623 |
Copyright terms: Public domain | W3C validator |