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Theorem rabbii 2675
Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv 2678. (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 2674 1  |-  { x  e.  A  |  ph }  =  { x  e.  A  |  ps }
Colors of variables: wff set class
Syntax hints:    <-> wb 104    = wceq 1332    e. wcel 1481   {crab 2421
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-rab 2426
This theorem is referenced by:  dfdif3  3189  suplocexpr  7555  dmtopon  12222
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