ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  vtocl2 Structured version   Unicode version

Theorem vtocl2 2603
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  _V
vtocl2.2  _V
vtocl2.3
vtocl2.4
Assertion
Ref Expression
vtocl2
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem vtocl2
StepHypRef Expression
1 vtocl2.1 . . . . . 6  _V
21isseti 2557 . . . . 5
3 vtocl2.2 . . . . . 6  _V
43isseti 2557 . . . . 5
5 eeanv 1804 . . . . . 6
6 vtocl2.3 . . . . . . . 8
76biimpd 132 . . . . . . 7
872eximi 1489 . . . . . 6
95, 8sylbir 125 . . . . 5
102, 4, 9mp2an 402 . . . 4
11 nfv 1418 . . . . 5  F/
121119.36-1 1560 . . . 4
1310, 12eximii 1490 . . 3
141319.36aiv 1778 . 2
15 vtocl2.4 . . 3
1615ax-gen 1335 . 2
1714, 16mpg 1337 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   wceq 1242  wex 1378   wcel 1390   _Vcvv 2551
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553
This theorem is referenced by:  caovord  5614
  Copyright terms: Public domain W3C validator