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Theorem bnj1464 29192
Description: Conversion of implicit substitution to explicit class substitution. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1464.1  |-  ( ps 
->  A. x ps )
bnj1464.2  |-  ( x  =  A  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
bnj1464  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  ps ) )
Distinct variable groups:    x, A    x, V
Allowed substitution hints:    ph( x)    ps( x)

Proof of Theorem bnj1464
StepHypRef Expression
1 bnj1464.1 . . 3  |-  ( ps 
->  A. x ps )
21nfi 1541 . 2  |-  F/ x ps
3 bnj1464.2 . 2  |-  ( x  =  A  ->  ( ph 
<->  ps ) )
42, 3sbciegf 3035 1  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1530    = wceq 1632    e. wcel 1696   [.wsbc 3004
This theorem is referenced by:  bnj1465  29193  bnj1468  29194
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-3an 936  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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