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Theorem rabbii 2601
Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv 2604. (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 2600 1  |-  { x  e.  A  |  ph }  =  { x  e.  A  |  ps }
Colors of variables: wff set class
Syntax hints:    <-> wb 103    = wceq 1287    e. wcel 1436   {crab 2359
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-rab 2364
This theorem is referenced by:  dfdif3  3099
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