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Theorem sbcbiiOLD 3219
Description: Formula-building inference rule for class substitution. (Contributed by NM, 11-Nov-2005.) (New usage is discouraged.) (Proof modification 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 3218 . 2  |-  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps )
32a1i 11 1  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    e. wcel 1726   [.wsbc 3163
This theorem is referenced by:  sbc3org  28678  trsbc  28687  sbcssOLD  28689  eqsbc3rVD  29014  bnj984  29385  bnj1452  29483
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-sbc 3164
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