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Theorem vtocl3gaf 3022
 Description: Implicit substitution of 3 classes for 3 set variables. (Contributed by NM, 10-Aug-2013.) (Revised by Mario Carneiro, 11-Oct-2016.)
Hypotheses
Ref Expression
vtocl3gaf.a
vtocl3gaf.b
vtocl3gaf.c
vtocl3gaf.d
vtocl3gaf.e
vtocl3gaf.f
vtocl3gaf.1
vtocl3gaf.2
vtocl3gaf.3
vtocl3gaf.4
vtocl3gaf.5
vtocl3gaf.6
vtocl3gaf.7
Assertion
Ref Expression
vtocl3gaf
Distinct variable groups:   ,,,   ,,,   ,,,
Allowed substitution hints:   (,,)   (,,)   (,,)   (,,)   (,,)   (,,)   (,,)

Proof of Theorem vtocl3gaf
StepHypRef Expression
1 vtocl3gaf.a . . 3
2 vtocl3gaf.b . . 3
3 vtocl3gaf.c . . 3
4 vtocl3gaf.d . . 3
5 vtocl3gaf.e . . 3
6 vtocl3gaf.f . . 3
71nfel1 2584 . . . . 5
8 nfv 1630 . . . . 5
9 nfv 1630 . . . . 5
107, 8, 9nf3an 1850 . . . 4
11 vtocl3gaf.1 . . . 4
1210, 11nfim 1833 . . 3
132nfel1 2584 . . . . 5
144nfel1 2584 . . . . 5
15 nfv 1630 . . . . 5
1613, 14, 15nf3an 1850 . . . 4
17 vtocl3gaf.2 . . . 4
1816, 17nfim 1833 . . 3
193nfel1 2584 . . . . 5
205nfel1 2584 . . . . 5
216nfel1 2584 . . . . 5
2219, 20, 21nf3an 1850 . . . 4
23 vtocl3gaf.3 . . . 4
2422, 23nfim 1833 . . 3
25 eleq1 2498 . . . . 5
26253anbi1d 1259 . . . 4
27 vtocl3gaf.4 . . . 4
2826, 27imbi12d 313 . . 3
29 eleq1 2498 . . . . 5
30293anbi2d 1260 . . . 4
31 vtocl3gaf.5 . . . 4
3230, 31imbi12d 313 . . 3
33 eleq1 2498 . . . . 5
34333anbi3d 1261 . . . 4
35 vtocl3gaf.6 . . . 4
3634, 35imbi12d 313 . . 3
37 vtocl3gaf.7 . . 3
381, 2, 3, 4, 5, 6, 12, 18, 24, 28, 32, 36, 37vtocl3gf 3016 . 2
3938pm2.43i 46 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   w3a 937  wnf 1554   wceq 1653   wcel 1726  wnfc 2561 This theorem is referenced by:  vtocl3ga  3023 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960
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