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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 2310 | . . . . 5 |
5 | nfv 1508 | . . . . 5 | |
6 | 4, 5 | nfan 1545 | . . . 4 |
7 | vtocl2gaf.1 | . . . 4 | |
8 | 6, 7 | nfim 1552 | . . 3 |
9 | 2 | nfel1 2310 | . . . . 5 |
10 | 3 | nfel1 2310 | . . . . 5 |
11 | 9, 10 | nfan 1545 | . . . 4 |
12 | vtocl2gaf.2 | . . . 4 | |
13 | 11, 12 | nfim 1552 | . . 3 |
14 | eleq1 2220 | . . . . 5 | |
15 | 14 | anbi1d 461 | . . . 4 |
16 | vtocl2gaf.3 | . . . 4 | |
17 | 15, 16 | imbi12d 233 | . . 3 |
18 | eleq1 2220 | . . . . 5 | |
19 | 18 | anbi2d 460 | . . . 4 |
20 | vtocl2gaf.4 | . . . 4 | |
21 | 19, 20 | imbi12d 233 | . . 3 |
22 | vtocl2gaf.5 | . . 3 | |
23 | 1, 2, 3, 8, 13, 17, 21, 22 | vtocl2gf 2774 | . 2 |
24 | 23 | pm2.43i 49 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wnf 1440 wcel 2128 wnfc 2286 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 |
This theorem is referenced by: vtocl2ga 2780 ovmpos 5944 ov2gf 5945 ovi3 5957 cnmptcom 12709 |
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