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Theorem sbcbii 2874
Description: Formula-building inference rule for class substitution. (Contributed by NM, 11-Nov-2005.)
Hypothesis
Ref Expression
sbcbii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
sbcbii  |-  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps )

Proof of Theorem sbcbii
StepHypRef Expression
1 sbcbii.1 . . . 4  |-  ( ph  <->  ps )
21a1i 9 . . 3  |-  ( T. 
->  ( ph  <->  ps )
)
32sbcbidv 2873 . 2  |-  ( T. 
->  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps ) )
43trud 1294 1  |-  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 103   T. wtru 1286   [.wsbc 2816
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-sbc 2817
This theorem is referenced by:  eqsbc3r  2875  sbc3an  2876  sbccomlem  2889  sbccom  2890  sbcabel  2896  csbco  2918  sbcnel12g  2924  sbcne12g  2925  sbccsbg  2935  sbccsb2g  2936  csbnestgf  2955  csbabg  2964  sbcssg  3358  sbcrel  4452  difopab  4497  sbcfung  4955  f1od2  5887  mpt2xopovel  5890  bezoutlemnewy  10529  bezoutlemstep  10530  bezoutlemmain  10531
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