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Theorem vtocl3 2911
 Description: Implicit substitution of classes for setvar 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 2865 . . . . . 6
3 vtocl3.2 . . . . . . 7
43isseti 2865 . . . . . 6
5 vtocl3.3 . . . . . . 7
65isseti 2865 . . . . . 6
7 eeeanv 1914 . . . . . . 7
8 vtocl3.4 . . . . . . . . . 10
98biimpd 198 . . . . . . . . 9
109eximi 1576 . . . . . . . 8
11102eximi 1577 . . . . . . 7
127, 11sylbir 204 . . . . . 6
132, 4, 6, 12mp3an 1277 . . . . 5
14 19.36v 1896 . . . . . 6
15142exbii 1583 . . . . 5
1613, 15mpbi 199 . . . 4
17 19.36v 1896 . . . . 5
1817exbii 1582 . . . 4
1916, 18mpbi 199 . . 3
201919.36aiv 1897 . 2
21 vtocl3.5 . . 3
2221gen2 1547 . 2
2320, 22mpg 1548 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   w3a 934  wal 1540  wex 1541   wceq 1642   wcel 1710  cvv 2859 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by: (None)
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