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Theorem bj-abbii 34783
Description: Remove dependency on ax-13 2004 from abbii 2588. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-abbii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
bj-abbii  |-  { x  |  ph }  =  {
x  |  ps }

Proof of Theorem bj-abbii
StepHypRef Expression
1 bj-abbi 34781 . 2  |-  ( A. x ( ph  <->  ps )  <->  { x  |  ph }  =  { x  |  ps } )
2 bj-abbii.1 . 2  |-  ( ph  <->  ps )
31, 2mpgbi 1626 1  |-  { x  |  ph }  =  {
x  |  ps }
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    = wceq 1398   {cab 2439
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446
This theorem is referenced by:  bj-rababwv  34863
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