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

Theorem vtoclgft 2598
Description: Closed theorem form of vtoclgf 2606. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 12-Oct-2016.)
Assertion
Ref Expression
vtoclgft  F/_  F/  V

Proof of Theorem vtoclgft
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elex 2560 . 2  V  _V
2 elisset 2562 . . . . 5  _V
323ad2ant3 926 . . . 4  F/_  F/  _V
4 nfnfc1 2178 . . . . . . 7  F/ F/_
5 nfcvd 2176 . . . . . . . 8  F/_  F/_
6 id 19 . . . . . . . 8  F/_  F/_
75, 6nfeqd 2189 . . . . . . 7  F/_  F/
8 eqeq1 2043 . . . . . . . 8
98a1i 9 . . . . . . 7  F/_
104, 7, 9cbvexd 1799 . . . . . 6  F/_
1110ad2antrr 457 . . . . 5  F/_  F/
12113adant3 923 . . . 4  F/_  F/  _V
133, 12mpbid 135 . . 3  F/_  F/  _V
14 bi1 111 . . . . . . . . 9
1514imim2i 12 . . . . . . . 8
1615com23 72 . . . . . . 7
1716imp 115 . . . . . 6
1817alanimi 1345 . . . . 5
19183ad2ant2 925 . . . 4  F/_  F/  _V
20 simp1r 928 . . . . 5  F/_  F/  _V  F/
21 19.23t 1564 . . . . 5  F/
2220, 21syl 14 . . . 4  F/_  F/  _V
2319, 22mpbid 135 . . 3  F/_  F/  _V
2413, 23mpd 13 . 2  F/_  F/  _V
251, 24syl3an3 1169 1  F/_  F/  V
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   w3a 884  wal 1240   wceq 1242   F/wnf 1346  wex 1378   wcel 1390   F/_wnfc 2162   _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-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553
This theorem is referenced by:  vtocldf  2599
  Copyright terms: Public domain W3C validator