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Theorem vtocl2gaf 2674
 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 2233 . . . . 5
5 nfv 1462 . . . . 5
64, 5nfan 1498 . . . 4
7 vtocl2gaf.1 . . . 4
86, 7nfim 1505 . . 3
92nfel1 2233 . . . . 5
103nfel1 2233 . . . . 5
119, 10nfan 1498 . . . 4
12 vtocl2gaf.2 . . . 4
1311, 12nfim 1505 . . 3
14 eleq1 2145 . . . . 5
1514anbi1d 453 . . . 4
16 vtocl2gaf.3 . . . 4
1715, 16imbi12d 232 . . 3
18 eleq1 2145 . . . . 5
1918anbi2d 452 . . . 4
20 vtocl2gaf.4 . . . 4
2119, 20imbi12d 232 . . 3
22 vtocl2gaf.5 . . 3
231, 2, 3, 8, 13, 17, 21, 22vtocl2gf 2669 . 2
2423pm2.43i 48 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103   wceq 1285  wnf 1390   wcel 1434  wnfc 2210 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612 This theorem is referenced by:  vtocl2ga  2675  ovmpt2s  5675  ov2gf  5676  ovi3  5688
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