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Theorem rabbii 2738
Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv 2741. (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 2737 1  |-  { x  e.  A  |  ph }  =  { x  e.  A  |  ps }
Colors of variables: wff set class
Syntax hints:    <-> wb 105    = wceq 1364    e. wcel 2160   {crab 2472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-rab 2477
This theorem is referenced by:  dfdif3  3260  suplocexpr  7759  dfrhm2  13529  dmtopon  14008
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