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Theorem abbi 2148
Description: Equivalent wff's correspond to equal class abstractions. (Contributed by NM, 25-Nov-2013.) (Revised by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
abbi  {  |  }  {  |  }

Proof of Theorem abbi
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfcleq 2031 . 2  {  |  }  {  |  } 
{  |  }  {  |  }
2 nfsab1 2027 . . . 4  F/  {  |  }
3 nfsab1 2027 . . . 4  F/  {  |  }
42, 3nfbi 1478 . . 3  F/  {  |  } 
{  |  }
5 nfv 1418 . . 3  F/
6 df-clab 2024 . . . . 5  {  |  }
7 sbequ12r 1652 . . . . 5
86, 7syl5bb 181 . . . 4  {  |  }
9 df-clab 2024 . . . . 5  {  |  }
10 sbequ12r 1652 . . . . 5
119, 10syl5bb 181 . . . 4  {  |  }
128, 11bibi12d 224 . . 3  {  |  } 
{  |  }
134, 5, 12cbval 1634 . 2  {  |  } 
{  |  }
141, 13bitr2i 174 1  {  |  }  {  |  }
Colors of variables: wff set class
Syntax hints:   wb 98  wal 1240   wceq 1242   wcel 1390  wsb 1642   {cab 2023
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
This theorem is referenced by:  abbii  2150  abbid  2151  rabbi  2481  dfiota2  4811  iotabi  4819  uniabio  4820
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