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Theorem bnj524 29042
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 3208 1  |-  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    e. wcel 1725   _Vcvv 2948   [.wsbc 3153
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-sbc 3154
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