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Mirrors > Home > ILE Home > Th. List > vtocl2gaf | Unicode version |
Description: Implicit substitution of 2 classes for 2 setvar variables. (Contributed by NM, 10-Aug-2013.) |
Ref | Expression |
---|---|
vtocl2gaf.a | |
vtocl2gaf.b | |
vtocl2gaf.c | |
vtocl2gaf.1 | |
vtocl2gaf.2 | |
vtocl2gaf.3 | |
vtocl2gaf.4 | |
vtocl2gaf.5 |
Ref | Expression |
---|---|
vtocl2gaf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtocl2gaf.a | . . 3 | |
2 | vtocl2gaf.b | . . 3 | |
3 | vtocl2gaf.c | . . 3 | |
4 | 1 | nfel1 2229 | . . . . 5 |
5 | nfv 1461 | . . . . 5 | |
6 | 4, 5 | nfan 1497 | . . . 4 |
7 | vtocl2gaf.1 | . . . 4 | |
8 | 6, 7 | nfim 1504 | . . 3 |
9 | 2 | nfel1 2229 | . . . . 5 |
10 | 3 | nfel1 2229 | . . . . 5 |
11 | 9, 10 | nfan 1497 | . . . 4 |
12 | vtocl2gaf.2 | . . . 4 | |
13 | 11, 12 | nfim 1504 | . . 3 |
14 | eleq1 2141 | . . . . 5 | |
15 | 14 | anbi1d 452 | . . . 4 |
16 | vtocl2gaf.3 | . . . 4 | |
17 | 15, 16 | imbi12d 232 | . . 3 |
18 | eleq1 2141 | . . . . 5 | |
19 | 18 | anbi2d 451 | . . . 4 |
20 | vtocl2gaf.4 | . . . 4 | |
21 | 19, 20 | imbi12d 232 | . . 3 |
22 | vtocl2gaf.5 | . . 3 | |
23 | 1, 2, 3, 8, 13, 17, 21, 22 | vtocl2gf 2660 | . 2 |
24 | 23 | pm2.43i 48 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wnf 1389 wcel 1433 wnfc 2206 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 |
This theorem is referenced by: vtocl2ga 2666 ovmpt2s 5644 ov2gf 5645 ovi3 5657 |
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