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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 2188 | . . . . 5 |
5 | nfv 1421 | . . . . 5 | |
6 | 4, 5 | nfan 1457 | . . . 4 |
7 | vtocl2gaf.1 | . . . 4 | |
8 | 6, 7 | nfim 1464 | . . 3 |
9 | 2 | nfel1 2188 | . . . . 5 |
10 | 3 | nfel1 2188 | . . . . 5 |
11 | 9, 10 | nfan 1457 | . . . 4 |
12 | vtocl2gaf.2 | . . . 4 | |
13 | 11, 12 | nfim 1464 | . . 3 |
14 | eleq1 2100 | . . . . 5 | |
15 | 14 | anbi1d 438 | . . . 4 |
16 | vtocl2gaf.3 | . . . 4 | |
17 | 15, 16 | imbi12d 223 | . . 3 |
18 | eleq1 2100 | . . . . 5 | |
19 | 18 | anbi2d 437 | . . . 4 |
20 | vtocl2gaf.4 | . . . 4 | |
21 | 19, 20 | imbi12d 223 | . . 3 |
22 | vtocl2gaf.5 | . . 3 | |
23 | 1, 2, 3, 8, 13, 17, 21, 22 | vtocl2gf 2615 | . 2 |
24 | 23 | pm2.43i 43 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 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-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: vtocl2ga 2621 ovmpt2s 5624 ov2gf 5625 ovi3 5637 |
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