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Theorem vtocl3gaf 3176
Description: Implicit substitution of 3 classes for 3 setvar 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:   , , ,   ,S, ,   , , ,

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 2635 . . . . 5
8 nfv 1707 . . . . 5
9 nfv 1707 . . . . 5
107, 8, 9nf3an 1930 . . . 4
11 vtocl3gaf.1 . . . 4
1210, 11nfim 1920 . . 3
132nfel1 2635 . . . . 5
144nfel1 2635 . . . . 5
15 nfv 1707 . . . . 5
1613, 14, 15nf3an 1930 . . . 4
17 vtocl3gaf.2 . . . 4
1816, 17nfim 1920 . . 3
193nfel1 2635 . . . . 5
205nfel1 2635 . . . . 5
216nfel1 2635 . . . . 5
2219, 20, 21nf3an 1930 . . . 4
23 vtocl3gaf.3 . . . 4
2422, 23nfim 1920 . . 3
25 eleq1 2529 . . . . 5
26253anbi1d 1303 . . . 4
27 vtocl3gaf.4 . . . 4
2826, 27imbi12d 320 . . 3
29 eleq1 2529 . . . . 5
30293anbi2d 1304 . . . 4
31 vtocl3gaf.5 . . . 4
3230, 31imbi12d 320 . . 3
33 eleq1 2529 . . . . 5
34333anbi3d 1305 . . . 4
35 vtocl3gaf.6 . . . 4
3634, 35imbi12d 320 . . 3
37 vtocl3gaf.7 . . 3
381, 2, 3, 4, 5, 6, 12, 18, 24, 28, 32, 36, 37vtocl3gf 3170 . 2
3938pm2.43i 47 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\w3a 973  =wceq 1395  F/wnf 1616  e.wcel 1818  F/_wnfc 2605
This theorem is referenced by:  vtocl3ga  3177
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111
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