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Theorem bnj524 28436
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 bnj524.1 . 2  |-  ( ph  <->  ps )
21sbcbii 3152 1  |-  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    e. wcel 1717   _Vcvv 2892   [.wsbc 3097
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-sbc 3098
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