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Theorem bnj525 33527
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 3387 . 2  |-  ( A  e.  _V  ->  ( [. A  /  x ]. ph  <->  ph ) )
31, 2ax-mp 5 1  |-  ( [. A  /  x ]. ph  <->  ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    e. wcel 1804   _Vcvv 3095   [.wsbc 3313
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-12 1840  ax-13 1985  ax-ext 2421
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-v 3097  df-sbc 3314
This theorem is referenced by:  bnj538OLD  33530  bnj976  33569  bnj91  33652  bnj92  33653  bnj523  33678  bnj539  33682  bnj540  33683  bnj1040  33761
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