Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  vtocl2 Unicode version

Theorem vtocl2 3162
 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:   ,,   ,,   ,,

Proof of Theorem vtocl2
StepHypRef Expression
1 vtocl2.1 . . . . . 6
21isseti 3115 . . . . 5
3 vtocl2.2 . . . . . 6
43isseti 3115 . . . . 5
5 eeanv 1988 . . . . . 6
6 vtocl2.3 . . . . . . . 8
76biimpd 207 . . . . . . 7
872eximi 1657 . . . . . 6
95, 8sylbir 213 . . . . 5
102, 4, 9mp2an 672 . . . 4
11 19.36v 1762 . . . . 5
1211exbii 1667 . . . 4
1310, 12mpbi 208 . . 3
141319.36iv 1763 . 2
15 vtocl2.4 . . 3
1615ax-gen 1618 . 2
1714, 16mpg 1620 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818   cvv 3109 This theorem is referenced by:  caovord  6486  sornom  8678  wloglei  10110  ipodrsima  15795  mpfind  18205  mclsppslem  28943  monotoddzzfi  30878 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
 Copyright terms: Public domain W3C validator