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Theorem vtocl3 3000
 Description: Implicit substitution of classes for set variables. (Contributed by NM, 3-Jun-1995.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Hypotheses
Ref Expression
vtocl3.1
vtocl3.2
vtocl3.3
vtocl3.4
vtocl3.5
Assertion
Ref Expression
vtocl3
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,
Allowed substitution hints:   (,,)

Proof of Theorem vtocl3
StepHypRef Expression
1 vtocl3.1 . . . . . . 7
21isseti 2954 . . . . . 6
3 vtocl3.2 . . . . . . 7
43isseti 2954 . . . . . 6
5 vtocl3.3 . . . . . . 7
65isseti 2954 . . . . . 6
7 eeeanv 1938 . . . . . . 7
8 vtocl3.4 . . . . . . . . . 10
98biimpd 199 . . . . . . . . 9
109eximi 1585 . . . . . . . 8
11102eximi 1586 . . . . . . 7
127, 11sylbir 205 . . . . . 6
132, 4, 6, 12mp3an 1279 . . . . 5
14 19.36v 1919 . . . . . 6
15142exbii 1593 . . . . 5
1613, 15mpbi 200 . . . 4
17 19.36v 1919 . . . . 5
1817exbii 1592 . . . 4
1916, 18mpbi 200 . . 3
201919.36aiv 1920 . 2
21 vtocl3.5 . . 3
2221gen2 1556 . 2
2320, 22mpg 1557 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   w3a 936  wal 1549  wex 1550   wceq 1652   wcel 1725  cvv 2948 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-3an 938  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-v 2950
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