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

Theorem eluniab 3555
Description: Membership in union of a class abstraction. (Contributed by NM, 11-Aug-1994.) (Revised by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
eluniab  U. {  |  }
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem eluniab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eluni 3546 . 2  U. {  |  }  {  |  }
2 nfv 1394 . . . 4  F/
3 nfsab1 2003 . . . 4  F/  {  |  }
42, 3nfan 1430 . . 3  F/  {  |  }
5 nfv 1394 . . 3  F/
6 eleq2 2074 . . . 4
7 eleq1 2073 . . . . 5  {  |  } 
{  |  }
8 abid 2001 . . . . 5  {  |  }
97, 8syl6bb 185 . . . 4  {  |  }
106, 9anbi12d 442 . . 3  {  |  }
114, 5, 10cbvex 1612 . 2  {  |  }
121, 11bitri 173 1  U. {  |  }
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98  wex 1354   wcel 1366   {cab 1999   U.cuni 3543
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-io 614  ax-5 1309  ax-7 1310  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-8 1368  ax-10 1369  ax-11 1370  ax-i12 1371  ax-bnd 1372  ax-4 1373  ax-17 1392  ax-i9 1396  ax-ial 1400  ax-i5r 1401  ax-ext 1995
This theorem depends on definitions:  df-bi 110  df-tru 1226  df-nf 1323  df-sb 1619  df-clab 2000  df-cleq 2006  df-clel 2009  df-nfc 2140  df-v 2528  df-uni 3544
This theorem is referenced by:  elunirab  3556  dfiun2g  3652  inuni  3872  snnex  4119  elfv  5089  unielxp  5711  tfrlem9  5845
  Copyright terms: Public domain W3C validator