reserve A for QC-alphabet;
reserve i,j,k for Nat;
reserve f for Substitution of A;

theorem Th8:
  for p being Element of QC-WFF(A) holds
  'not' p is Element of CQC-WFF(A) iff p is Element of CQC-WFF(A)
proof
  let p be Element of QC-WFF(A);
  thus 'not' p is Element of CQC-WFF(A) implies p is Element of CQC-WFF(A)
  proof
    assume
A1: 'not' p is Element of CQC-WFF(A);
    then Free 'not' p = {} by Th4;
    then
A2: Free p = {} by QC_LANG3:55;
    Fixed 'not' p = {} by A1,Th4;
    then Fixed p = {} by QC_LANG3:65;
    hence thesis by A2,Th4;
  end;
  assume p is Element of CQC-WFF(A);
  then reconsider r = p as Element of CQC-WFF(A);
  Fixed r = {} by Th4;
  then
A3: Fixed 'not' r = {} by QC_LANG3:65;
  Free r = {} by Th4;
  then Free 'not' r = {} by QC_LANG3:55;
  hence thesis by A3,Th4;
end;
