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 Th3:
  p => q in TAUT(A) & q => r in TAUT(A) implies p => r in TAUT(A)
proof
  assume that
A1: p => q in TAUT(A) and
A2: q => r in TAUT(A);
  (p => q) => ((q => r) => (p => r)) in TAUT(A) by Th1;
  then (q => r) => (p => r) in TAUT(A) by A1,CQC_THE1:46;
  hence thesis by A2,CQC_THE1:46;
end;
