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Theorem vtocl3 2627
 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 2580 . . . . . 6
3 vtocl3.2 . . . . . . 7
43isseti 2580 . . . . . 6
5 vtocl3.3 . . . . . . 7
65isseti 2580 . . . . . 6
7 eeeanv 1824 . . . . . . 7
8 vtocl3.4 . . . . . . . . . 10
98biimpd 136 . . . . . . . . 9
109eximi 1507 . . . . . . . 8
11102eximi 1508 . . . . . . 7
127, 11sylbir 129 . . . . . 6
132, 4, 6, 12mp3an 1243 . . . . 5
14 nfv 1437 . . . . . . 7
151419.36-1 1579 . . . . . 6
16152eximi 1508 . . . . 5
1713, 16ax-mp 7 . . . 4
18 nfv 1437 . . . . 5
191819.36-1 1579 . . . 4
2017, 19eximii 1509 . . 3
212019.36aiv 1797 . 2
22 vtocl3.5 . . 3
2322gen2 1355 . 2
2421, 23mpg 1356 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 102   w3a 896  wal 1257   wceq 1259  wex 1397   wcel 1409  cvv 2574 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-3an 898  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-v 2576 This theorem is referenced by: (None)
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