ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  dfuni2 Structured version   Unicode version

Theorem dfuni2 3545
Description: Alternate definition of class union. (Contributed by NM, 28-Jun-1998.)
Assertion
Ref Expression
dfuni2  U.  {  |  }
Distinct variable group:   ,,

Proof of Theorem dfuni2
StepHypRef Expression
1 df-uni 3544 . 2  U.  {  |  }
2 exancom 1472 . . . 4
3 df-rex 2281 . . . 4
42, 3bitr4i 176 . . 3
54abbii 2126 . 2  {  |  }  {  |  }
61, 5eqtri 2033 1  U.  {  |  }
Colors of variables: wff set class
Syntax hints:   wa 97   wceq 1223  wex 1354   wcel 1366   {cab 1999  wrex 2276   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-5 1309  ax-7 1310  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-8 1368  ax-11 1370  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-rex 2281  df-uni 3544
This theorem is referenced by:  nfuni  3549  nfunid  3550  unieq  3552  uniiun  3673
  Copyright terms: Public domain W3C validator