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Theorem vtocl4ga 3163
 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:   ,,,,   ,,,   ,,   ,   ,,,,   ,,,,   ,,,,   ,,,,   ,   ,   ,   ,
Allowed substitution hints:   (,,,)   (,,)   (,,)   (,,)   (,,)   ()   (,)   (,,)

Proof of Theorem vtocl4ga
StepHypRef Expression
1 eleq1 2513 . . . . . 6
21anbi1d 704 . . . . 5
32anbi1d 704 . . . 4
4 vtocl4ga.1 . . . 4
53, 4imbi12d 320 . . 3
6 eleq1 2513 . . . . . 6
76anbi2d 703 . . . . 5
87anbi1d 704 . . . 4
9 vtocl4ga.2 . . . 4
108, 9imbi12d 320 . . 3
11 eleq1 2513 . . . . . 6
1211anbi1d 704 . . . . 5
1312anbi2d 703 . . . 4
14 vtocl4ga.3 . . . 4
1513, 14imbi12d 320 . . 3
16 eleq1 2513 . . . . . 6
1716anbi2d 703 . . . . 5
1817anbi2d 703 . . . 4
19 vtocl4ga.4 . . . 4
2018, 19imbi12d 320 . . 3
21 vtocl4ga.5 . . 3
225, 10, 15, 20, 21vtocl4g 3162 . 2
2322pm2.43i 47 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1381   wcel 1802 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-v 3095 This theorem is referenced by:  wrd2ind  12677
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