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Theorem vtocl3ga 3177
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:   , , ,   , ,   ,   , , ,   , , ,   ,S, ,   ,   ,   ,

Proof of Theorem vtocl3ga
StepHypRef Expression
1 nfcv 2619 . 2
2 nfcv 2619 . 2
3 nfcv 2619 . 2
4 nfcv 2619 . 2
5 nfcv 2619 . 2
6 nfcv 2619 . 2
7 nfv 1707 . 2
8 nfv 1707 . 2
9 nfv 1707 . 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 3176 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\w3a 973  =wceq 1395  e.wcel 1818
This theorem is referenced by:  preq12bg  4209  prel12g  4210  pocl  4812  jensenlem2  23317
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-3an 975  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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