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Theorem bnj525 29083
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 3069 . 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 176    e. wcel 1696   _Vcvv 2801   [.wsbc 3004
This theorem is referenced by:  bnj538  29085  bnj976  29125  bnj91  29209  bnj92  29210  bnj523  29235  bnj539  29239  bnj540  29240  bnj1040  29318
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-sbc 3005
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