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Theorem vtocl3ga 2690
 Description: Implicit substitution of 3 classes for 3 setvar variables. (Contributed by NM, 20-Aug-1995.)
Hypotheses
Ref Expression
vtocl3ga.1
vtocl3ga.2
vtocl3ga.3
vtocl3ga.4
Assertion
Ref Expression
vtocl3ga
Distinct variable groups:   ,,,   ,,   ,   ,,,   ,,,   ,,,   ,   ,   ,
Allowed substitution hints:   (,,)   (,)   (,)   (,)   ()   (,)

Proof of Theorem vtocl3ga
StepHypRef Expression
1 nfcv 2229 . 2
2 nfcv 2229 . 2
3 nfcv 2229 . 2
4 nfcv 2229 . 2
5 nfcv 2229 . 2
6 nfcv 2229 . 2
7 nfv 1467 . 2
8 nfv 1467 . 2
9 nfv 1467 . 2
10 vtocl3ga.1 . 2
11 vtocl3ga.2 . 2
12 vtocl3ga.3 . 2
13 vtocl3ga.4 . 2
141, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13vtocl3gaf 2689 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   w3a 925   wceq 1290   wcel 1439 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622 This theorem is referenced by:  preq12bg  3623  pocl  4139  sowlin  4156
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