ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sbcbii Unicode version

Theorem sbcbii 2968
Description: Formula-building inference 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 2967 . 2  |-  ( T. 
->  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps ) )
43mptru 1340 1  |-  ( [. A  /  x ]. ph  <->  [. A  /  x ]. ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 104   T. wtru 1332   [.wsbc 2909
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-sbc 2910
This theorem is referenced by:  eqsbc3r  2969  sbc3an  2970  sbccomlem  2983  sbccom  2984  sbcabel  2990  csbco  3013  sbcnel12g  3019  sbcne12g  3020  sbccsbg  3031  sbccsb2g  3032  csbnestgf  3052  csbabg  3061  sbcssg  3472  sbcrel  4625  difopab  4672  sbcfung  5147  f1od2  6132  mpoxopovel  6138  bezoutlemnewy  11691  bezoutlemstep  11692  bezoutlemmain  11693
  Copyright terms: Public domain W3C validator