reserve A for QC-alphabet;
reserve p, q, r, s, t for Element of CQC-WFF(A);
reserve X for Subset of CQC-WFF(A);

theorem Th24:
  ('not' p => 'not' q) => (q => p) in TAUT(A)
proof
  q => ('not' q => 'not' VERUM(A)) in TAUT(A) &
  ('not' q => 'not' VERUM(A)) => ((
  'not' p => 'not' q) => ('not' p => 'not' VERUM(A))) in TAUT(A)
  by Th9,CQC_THE1:43;
  then
A1: q => (('not' p => 'not' q) => ('not' p => 'not' VERUM(A))) in TAUT(A)
  by Th3;
  q => (('not' p => 'not' VERUM(A)) => p) in TAUT(A) by Lm24,Th13;
  then q => (('not' p => 'not' q) => p) in TAUT(A) by A1,Th22;
  hence thesis by Th15;
end;
