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Theorem vtocl2gaf 3174
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:   , ,   , ,

Proof of Theorem vtocl2gaf
StepHypRef Expression
1 vtocl2gaf.a . . 3
2 vtocl2gaf.b . . 3
3 vtocl2gaf.c . . 3
41nfel1 2635 . . . . 5
5 nfv 1707 . . . . 5
64, 5nfan 1928 . . . 4
7 vtocl2gaf.1 . . . 4
86, 7nfim 1920 . . 3
92nfel1 2635 . . . . 5
103nfel1 2635 . . . . 5
119, 10nfan 1928 . . . 4
12 vtocl2gaf.2 . . . 4
1311, 12nfim 1920 . . 3
14 eleq1 2529 . . . . 5
1514anbi1d 704 . . . 4
16 vtocl2gaf.3 . . . 4
1715, 16imbi12d 320 . . 3
18 eleq1 2529 . . . . 5
1918anbi2d 703 . . . 4
20 vtocl2gaf.4 . . . 4
2119, 20imbi12d 320 . . 3
22 vtocl2gaf.5 . . 3
231, 2, 3, 8, 13, 17, 21, 22vtocl2gf 3169 . 2
2423pm2.43i 47 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  F/wnf 1616  e.wcel 1818  F/_wnfc 2605
This theorem is referenced by:  vtocl2ga  3175  ovmpt2s  6426  ov2gf  6427  ov3  6439  pwfseqlem2  9058  cnmptcom  20179
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-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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