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Theorem vtocl2 2767
 Description: Implicit substitution of classes for setvar variables. (Contributed by NM, 26-Jul-1995.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Hypotheses
Ref Expression
vtocl2.1
vtocl2.2
vtocl2.3
vtocl2.4
Assertion
Ref Expression
vtocl2
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem vtocl2
StepHypRef Expression
1 vtocl2.1 . . . . . 6
21isseti 2720 . . . . 5
3 vtocl2.2 . . . . . 6
43isseti 2720 . . . . 5
5 eeanv 1912 . . . . . 6
6 vtocl2.3 . . . . . . . 8
76biimpd 143 . . . . . . 7
872eximi 1581 . . . . . 6
95, 8sylbir 134 . . . . 5
102, 4, 9mp2an 423 . . . 4
11 nfv 1508 . . . . 5
121119.36-1 1653 . . . 4
1310, 12eximii 1582 . . 3
141319.36aiv 1881 . 2
15 vtocl2.4 . . 3
1615ax-gen 1429 . 2
1714, 16mpg 1431 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1333   wceq 1335  wex 1472   wcel 2128  cvv 2712 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-v 2714 This theorem is referenced by:  undifexmid  4154  caovord  5989  ctssexmid  7087
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