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Theorem iunab 3697
Description: The indexed union of a class abstraction. (Contributed by NM, 27-Dec-2004.)
Assertion
Ref Expression
iunab  U_  {  |  }  {  |  }
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem iunab
StepHypRef Expression
1 nfcv 2178 . . . 4  F/_
2 nfab1 2180 . . . 4  F/_ {  |  }
31, 2nfiunxy 3677 . . 3  F/_ U_  {  |  }
4 nfab1 2180 . . 3  F/_ {  |  }
53, 4cleqf 2201 . 2  U_  {  |  }  {  |  } 
U_  {  |  }  {  |  }
6 abid 2028 . . . 4  {  |  }
76rexbii 2328 . . 3  {  |  }
8 eliun 3655 . . 3  U_  {  |  }  {  |  }
9 abid 2028 . . 3  {  |  }
107, 8, 93bitr4i 201 . 2  U_  {  |  }  {  |  }
115, 10mpgbir 1342 1  U_  {  |  }  {  |  }
Colors of variables: wff set class
Syntax hints:   wb 98   wceq 1243   wcel 1393   {cab 2026  wrex 2304   U_ciun 3651
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2308  df-rex 2309  df-v 2556  df-iun 3653
This theorem is referenced by:  iunrab  3698  iunid  3706  dfimafn2  5169
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