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Theorem bnj525 29044
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj525.1  |-  A  e. 
_V
Assertion
Ref Expression
bnj525  |-  ( [. A  /  x ]. ph  <->  ph )
Distinct variable group:    ph, x
Allowed substitution hint:    A( x)

Proof of Theorem bnj525
StepHypRef Expression
1 bnj525.1 . 2  |-  A  e. 
_V
2 sbcg 3219 . 2  |-  ( A  e.  _V  ->  ( [. A  /  x ]. ph  <->  ph ) )
31, 2ax-mp 8 1  |-  ( [. A  /  x ]. ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    e. wcel 1725   _Vcvv 2949   [.wsbc 3154
This theorem is referenced by:  bnj538  29046  bnj976  29086  bnj91  29170  bnj92  29171  bnj523  29196  bnj539  29200  bnj540  29201  bnj1040  29279
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 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2951  df-sbc 3155
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