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Mirrors > Home > ILE Home > Th. List > vtoclgaf | Unicode version |
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 17-Feb-2006.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
vtoclgaf.1 | |
vtoclgaf.2 | |
vtoclgaf.3 | |
vtoclgaf.4 |
Ref | Expression |
---|---|
vtoclgaf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtoclgaf.1 | . . 3 | |
2 | 1 | nfel1 2188 | . . . 4 |
3 | vtoclgaf.2 | . . . 4 | |
4 | 2, 3 | nfim 1464 | . . 3 |
5 | eleq1 2100 | . . . 4 | |
6 | vtoclgaf.3 | . . . 4 | |
7 | 5, 6 | imbi12d 223 | . . 3 |
8 | vtoclgaf.4 | . . 3 | |
9 | 1, 4, 7, 8 | vtoclgf 2612 | . 2 |
10 | 9 | pm2.43i 43 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 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: vtoclga 2619 ssiun2s 3701 tfis 4306 fvmptf 5263 fmptco 5330 |
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