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Theorem bnj1464 29727
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 1682 . 2  |-  F/ x ps
3 bnj1464.2 . 2  |-  ( x  =  A  ->  ( ph 
<->  ps ) )
42, 3sbciegf 3287 1  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 189   A.wal 1450    = wceq 1452    e. wcel 1904   [.wsbc 3255
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104  ax-ext 2451
This theorem depends on definitions:  df-bi 190  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-v 3033  df-sbc 3256
This theorem is referenced by:  bnj1465  29728  bnj1468  29729
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