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Theorem abbi 2129
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 2012 . 2  {  |  }  {  |  } 
{  |  }  {  |  }
2 nfsab1 2008 . . . 4  F/  {  |  }
3 nfsab1 2008 . . . 4  F/  {  |  }
42, 3nfbi 1459 . . 3  F/  {  |  } 
{  |  }
5 nfv 1398 . . 3  F/
6 df-clab 2005 . . . . 5  {  |  }
7 sbequ12r 1633 . . . . 5
86, 7syl5bb 181 . . . 4  {  |  }
9 df-clab 2005 . . . . 5  {  |  }
10 sbequ12r 1633 . . . . 5
119, 10syl5bb 181 . . . 4  {  |  }
128, 11bibi12d 224 . . 3  {  |  } 
{  |  }
134, 5, 12cbval 1615 . 2  {  |  } 
{  |  }
141, 13bitr2i 174 1  {  |  }  {  |  }
Colors of variables: wff set class
Syntax hints:   wb 98  wal 1224   wceq 1226   wcel 1370  wsb 1623   {cab 2004
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 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-11 1374  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011
This theorem is referenced by:  abbii  2131  abbid  2132  rabbi  2461  dfiota2  4791  iotabi  4799  uniabio  4800
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