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Theorem iotauni 4825
Description: Equivalence between two different forms of  iota. (Contributed by Andrew Salmon, 12-Jul-2011.)
Assertion
Ref Expression
iotauni  iota 
U. {  |  }

Proof of Theorem iotauni
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-eu 1903 . 2
2 iotaval 4824 . . . 4  iota
3 uniabio 4823 . . . 4  U. {  |  }
42, 3eqtr4d 2075 . . 3  iota 
U. {  |  }
54exlimiv 1489 . 2  iota  U. {  |  }
61, 5sylbi 114 1  iota 
U. {  |  }
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1241   wceq 1243  wex 1381  weu 1900   {cab 2026   U.cuni 3574   iotacio 4811
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-eu 1903  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2309  df-v 2556  df-sbc 2762  df-un 2919  df-sn 3376  df-pr 3377  df-uni 3575  df-iota 4813
This theorem is referenced by:  iotaint  4826  fveu  5116  riotauni  5420
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