Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2293 | . . . . 5 |
5 | nfv 1509 | . . . . 5 | |
6 | 4, 5 | nfan 1545 | . . . 4 |
7 | vtocl2gaf.1 | . . . 4 | |
8 | 6, 7 | nfim 1552 | . . 3 |
9 | 2 | nfel1 2293 | . . . . 5 |
10 | 3 | nfel1 2293 | . . . . 5 |
11 | 9, 10 | nfan 1545 | . . . 4 |
12 | vtocl2gaf.2 | . . . 4 | |
13 | 11, 12 | nfim 1552 | . . 3 |
14 | eleq1 2203 | . . . . 5 | |
15 | 14 | anbi1d 461 | . . . 4 |
16 | vtocl2gaf.3 | . . . 4 | |
17 | 15, 16 | imbi12d 233 | . . 3 |
18 | eleq1 2203 | . . . . 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 2751 | . 2 |
24 | 23 | pm2.43i 49 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1332 wnf 1437 wcel 1481 wnfc 2269 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 |
This theorem is referenced by: vtocl2ga 2757 ovmpos 5902 ov2gf 5903 ovi3 5915 cnmptcom 12506 |
Copyright terms: Public domain | W3C validator |