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Theorem inrab2 3204
Description: Intersection with a restricted class abstraction. (Contributed by NM, 19-Nov-2007.)
Assertion
Ref Expression
inrab2  {  |  }  i^i  {  i^i  |  }
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem inrab2
StepHypRef Expression
1 df-rab 2309 . . 3  {  |  }  {  |  }
2 abid2 2155 . . . 4  {  |  }
32eqcomi 2041 . . 3  {  |  }
41, 3ineq12i 3130 . 2  {  |  }  i^i  {  |  }  i^i  {  |  }
5 df-rab 2309 . . 3  {  i^i  |  }  {  |  i^i  }
6 inab 3199 . . . 4  {  |  }  i^i  {  |  }  {  |  }
7 elin 3120 . . . . . . 7  i^i
87anbi1i 431 . . . . . 6  i^i
9 an32 496 . . . . . 6
108, 9bitri 173 . . . . 5  i^i
1110abbii 2150 . . . 4  {  |  i^i  }  {  |  }
126, 11eqtr4i 2060 . . 3  {  |  }  i^i  {  |  }  {  |  i^i  }
135, 12eqtr4i 2060 . 2  {  i^i  |  }  {  |  }  i^i  {  |  }
144, 13eqtr4i 2060 1  {  |  }  i^i  {  i^i  |  }
Colors of variables: wff set class
Syntax hints:   wa 97   wceq 1242   wcel 1390   {cab 2023   {crab 2304    i^i cin 2910
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-bndl 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-rab 2309  df-v 2553  df-in 2918
This theorem is referenced by:  iooval2  8554  fzval2  8647
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