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Theorem rabbii 2598
Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv 2601. (Contributed by Peter Mazsa, 1-Nov-2019.)
Hypothesis
Ref Expression
rabbii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
rabbii  |-  { x  e.  A  |  ph }  =  { x  e.  A  |  ps }

Proof of Theorem rabbii
StepHypRef Expression
1 rabbii.1 . . 3  |-  ( ph  <->  ps )
21a1i 9 . 2  |-  ( x  e.  A  ->  ( ph 
<->  ps ) )
32rabbiia 2597 1  |-  { x  e.  A  |  ph }  =  { x  e.  A  |  ps }
Colors of variables: wff set class
Syntax hints:    <-> wb 103    = wceq 1285    e. wcel 1434   {crab 2357
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-rab 2362
This theorem is referenced by:  dfdif3  3094
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