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 Th1:
  (p => q) => ((q => r) => (p => r)) in TAUT(A)
proof
  (p => q) => ('not'(q '&' 'not' r) => 'not'(p '&' 'not' r)) in TAUT(A) by
CQC_THE1:44;
  then (p => q) => ((q => r) => 'not'(p '&' 'not' r)) in TAUT(A)
  by QC_LANG2:def 2;
  hence thesis by QC_LANG2:def 2;
end;
