ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  cgsex2g Unicode version

Theorem cgsex2g 2584
Description: Implicit substitution inference for general classes. (Contributed by NM, 26-Jul-1995.)
Hypotheses
Ref Expression
cgsex2g.1
cgsex2g.2
Assertion
Ref Expression
cgsex2g  V  W
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)    V(,)    W(,)

Proof of Theorem cgsex2g
StepHypRef Expression
1 cgsex2g.2 . . . 4
21biimpa 280 . . 3
32exlimivv 1773 . 2
4 elisset 2562 . . . . . 6  V
5 elisset 2562 . . . . . 6  W
64, 5anim12i 321 . . . . 5  V  W
7 eeanv 1804 . . . . 5
86, 7sylibr 137 . . . 4  V  W
9 cgsex2g.1 . . . . 5
1092eximi 1489 . . . 4
118, 10syl 14 . . 3  V  W
121biimprcd 149 . . . . 5
1312ancld 308 . . . 4
14132eximdv 1759 . . 3
1511, 14syl5com 26 . 2  V  W
163, 15impbid2 131 1  V  W
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1242  wex 1378   wcel 1390
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: (None)
  Copyright terms: Public domain W3C validator