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Theorem sbcbiiOLD 3047
Description: Formula-building inference rule for class substitution. (Contributed by NM, 11-Nov-2005.) (New usage is discouraged.)
Hypothesis
Ref Expression
sbcbii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
sbcbiiOLD  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps ) )

Proof of Theorem sbcbiiOLD
StepHypRef Expression
1 sbcbii.1 . . 3  |-  ( ph  <->  ps )
21sbcbii 3046 . 2  |-  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps )
32a1i 10 1  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    e. wcel 1684   [.wsbc 2991
This theorem is referenced by:  isibg2  26110  2sbcrex  26864  sbc3org  28295  trsbc  28304  sbcssOLD  28306  eqsbc3rVD  28616  bnj89  28747  bnj524  28766  bnj984  28984  bnj1452  29082
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-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-sbc 2992
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