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Theorem bnj524 28139
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj524.1  |-  ( ph  <->  ps )
bnj524.2  |-  A  e. 
_V
Assertion
Ref Expression
bnj524  |-  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps )

Proof of Theorem bnj524
StepHypRef Expression
1 bnj524.2 . 2  |-  A  e. 
_V
2 bnj524.1 . . 3  |-  ( ph  <->  ps )
32sbcbiiOLD 3047 . 2  |-  ( A  e.  _V  ->  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps ) )
41, 3ax-mp 8 1  |-  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    e. wcel 1684   _Vcvv 2788   [.wsbc 2991
This theorem is referenced by:  bnj538  28142  bnj919  28170  bnj91  28266  bnj92  28267  bnj106  28273  bnj121  28275  bnj125  28277  bnj126  28278  bnj130  28279  bnj153  28285  bnj207  28286  bnj523  28292  bnj526  28293  bnj539  28296  bnj540  28297  bnj611  28323  bnj934  28340  bnj1000  28346
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-sbc 2992
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