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Theorem bnj525 28140
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 3056 . 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 1684   _Vcvv 2788   [.wsbc 2991
This theorem is referenced by:  bnj538  28142  bnj976  28182  bnj91  28266  bnj92  28267  bnj523  28292  bnj539  28296  bnj540  28297  bnj1040  28375
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-sbc 2992
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