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Theorem rabbiia 2541
Description: Equivalent wff's yield equal restricted class abstractions (inference rule). (Contributed by NM, 22-May-1999.)
Hypothesis
Ref Expression
rabbiia.1
Assertion
Ref Expression
rabbiia  {  |  }  {  |  }

Proof of Theorem rabbiia
StepHypRef Expression
1 rabbiia.1 . . . 4
21pm5.32i 427 . . 3
32abbii 2150 . 2  {  |  }  {  |  }
4 df-rab 2309 . 2  {  |  }  {  |  }
5 df-rab 2309 . 2  {  |  }  {  |  }
63, 4, 53eqtr4i 2067 1  {  |  }  {  |  }
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1242   wcel 1390   {cab 2023   {crab 2304
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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  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-rab 2309
This theorem is referenced by:  bm2.5ii  4188  fndmdifcom  5216  cauappcvgprlemladdru  6628  cauappcvgprlemladdrl  6629  cauappcvgpr  6634  caucvgprlemcl  6647  caucvgprlemladdrl  6649  caucvgpr  6653  ioopos  8589
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