Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-abbii Structured version   Visualization version   Unicode version

Theorem bj-abbii 31436
Description: Remove dependency on ax-13 2101 from abbii 2577. (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 31434 . 2  |-  ( A. x ( ph  <->  ps )  <->  { x  |  ph }  =  { x  |  ps } )
2 bj-abbii.1 . 2  |-  ( ph  <->  ps )
31, 2mpgbi 1682 1  |-  { x  |  ph }  =  {
x  |  ps }
Colors of variables: wff setvar class
Syntax hints:    <-> wb 189    = wceq 1454   {cab 2447
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-10 1925  ax-11 1930  ax-12 1943  ax-ext 2441
This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1457  df-ex 1674  df-nf 1678  df-sb 1808  df-clab 2448  df-cleq 2454
This theorem is referenced by:  bj-rababwv  31520
  Copyright terms: Public domain W3C validator