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Theorem elunirab 3584
Description: Membership in union of a class abstraction. (Contributed by NM, 4-Oct-2006.)
Assertion
Ref Expression
elunirab  U. {  |  }
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem elunirab
StepHypRef Expression
1 eluniab 3583 . 2  U. {  |  }
2 df-rab 2309 . . . 4  {  |  }  {  |  }
32unieqi 3581 . . 3  U. {  |  }  U. {  |  }
43eleq2i 2101 . 2  U. {  |  }  U. {  |  }
5 df-rex 2306 . . 3
6 an12 495 . . . 4
76exbii 1493 . . 3
85, 7bitri 173 . 2
91, 4, 83bitr4i 201 1  U. {  |  }
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98  wex 1378   wcel 1390   {cab 2023  wrex 2301   {crab 2304   U.cuni 3571
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-rab 2309  df-v 2553  df-uni 3572
This theorem is referenced by: (None)
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