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 Th59:
  X|- p => q & X|- q => r implies X|- p => r
proof
  assume that
A1: X|- p => q and
A2: X|- q => r;
  X|- (p => q) => ((q => r) => (p => r)) by CQC_THE1:59;
  then X|- (q => r) => (p => r) by A1,CQC_THE1:55;
  hence thesis by A2,CQC_THE1:55;
end;
