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Theorem vtocl2gaf 2921
 Description: Implicit substitution of 2 classes for 2 setvar variables. (Contributed by NM, 10-Aug-2013.)
Hypotheses
Ref Expression
vtocl2gaf.a
vtocl2gaf.b
vtocl2gaf.c
vtocl2gaf.1
vtocl2gaf.2
vtocl2gaf.3
vtocl2gaf.4
vtocl2gaf.5
Assertion
Ref Expression
vtocl2gaf
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)   (,)   (,)

Proof of Theorem vtocl2gaf
StepHypRef Expression
1 vtocl2gaf.a . . 3
2 vtocl2gaf.b . . 3
3 vtocl2gaf.c . . 3
41nfel1 2499 . . . . 5
5 nfv 1619 . . . . 5
64, 5nfan 1824 . . . 4
7 vtocl2gaf.1 . . . 4
86, 7nfim 1813 . . 3
92nfel1 2499 . . . . 5
103nfel1 2499 . . . . 5
119, 10nfan 1824 . . . 4
12 vtocl2gaf.2 . . . 4
1311, 12nfim 1813 . . 3
14 eleq1 2413 . . . . 5
1514anbi1d 685 . . . 4
16 vtocl2gaf.3 . . . 4
1715, 16imbi12d 311 . . 3
18 eleq1 2413 . . . . 5
1918anbi2d 684 . . . 4
20 vtocl2gaf.4 . . . 4
2119, 20imbi12d 311 . . 3
22 vtocl2gaf.5 . . 3
231, 2, 3, 8, 13, 17, 21, 22vtocl2gf 2916 . 2
2423pm2.43i 43 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wnf 1544   wceq 1642   wcel 1710  wnfc 2476 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861 This theorem is referenced by:  vtocl2ga  2922  ov3  5599  ov2gf  5711
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