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Theorem vtocl2gaf 2725
 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 2267 . . . . 5
5 nfv 1491 . . . . 5
64, 5nfan 1527 . . . 4
7 vtocl2gaf.1 . . . 4
86, 7nfim 1534 . . 3
92nfel1 2267 . . . . 5
103nfel1 2267 . . . . 5
119, 10nfan 1527 . . . 4
12 vtocl2gaf.2 . . . 4
1311, 12nfim 1534 . . 3
14 eleq1 2178 . . . . 5
1514anbi1d 458 . . . 4
16 vtocl2gaf.3 . . . 4
1715, 16imbi12d 233 . . 3
18 eleq1 2178 . . . . 5
1918anbi2d 457 . . . 4
20 vtocl2gaf.4 . . . 4
2119, 20imbi12d 233 . . 3
22 vtocl2gaf.5 . . 3
231, 2, 3, 8, 13, 17, 21, 22vtocl2gf 2720 . 2
2423pm2.43i 49 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1314  wnf 1419   wcel 1463  wnfc 2243 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660 This theorem is referenced by:  vtocl2ga  2726  ovmpos  5860  ov2gf  5861  ovi3  5873  cnmptcom  12362
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