New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  cgsexg Unicode version

Theorem cgsexg 2890
 Description: Implicit substitution inference for general classes. (Contributed by NM, 26-Aug-2007.)
Hypotheses
Ref Expression
cgsexg.1
cgsexg.2
Assertion
Ref Expression
cgsexg
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem cgsexg
StepHypRef Expression
1 cgsexg.2 . . . 4
21biimpa 470 . . 3
32exlimiv 1634 . 2
4 elisset 2869 . . . 4
5 cgsexg.1 . . . . 5
65eximi 1576 . . . 4
74, 6syl 15 . . 3
81biimprcd 216 . . . . 5
98ancld 536 . . . 4
109eximdv 1622 . . 3
117, 10syl5com 26 . 2
123, 11impbid2 195 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator