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Theorem vtocl4ga 3179
Description: Implicit substitution of 4 classes for 4 setvar variables. (Contributed by AV, 22-Jan-2019.)
Hypotheses
Ref Expression
vtocl4ga.1
vtocl4ga.2
vtocl4ga.3
vtocl4ga.4
vtocl4ga.5
Assertion
Ref Expression
vtocl4ga
Distinct variable groups:   , , , ,   , , ,   , ,   ,   , , , ,   ,S, , ,   , , , ,   ,Q, , ,   ,   ,   ,   ,

Proof of Theorem vtocl4ga
StepHypRef Expression
1 eleq1 2529 . . . . . 6
21anbi1d 704 . . . . 5
32anbi1d 704 . . . 4
4 vtocl4ga.1 . . . 4
53, 4imbi12d 320 . . 3
6 eleq1 2529 . . . . . 6
76anbi2d 703 . . . . 5
87anbi1d 704 . . . 4
9 vtocl4ga.2 . . . 4
108, 9imbi12d 320 . . 3
11 eleq1 2529 . . . . . 6
1211anbi1d 704 . . . . 5
1312anbi2d 703 . . . 4
14 vtocl4ga.3 . . . 4
1513, 14imbi12d 320 . . 3
16 eleq1 2529 . . . . . 6
1716anbi2d 703 . . . . 5
1817anbi2d 703 . . . 4
19 vtocl4ga.4 . . . 4
2018, 19imbi12d 320 . . 3
21 vtocl4ga.5 . . 3
225, 10, 15, 20, 21vtocl4g 3178 . 2
2322pm2.43i 47 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818
This theorem is referenced by:  wrd2ind  12703
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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