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
  X |- p => (p => q) implies X |- p => q
proof
  assume
A1: X |- p => (p => q);
  X|- (p => (p => q)) => (p => q) by CQC_THE1:59;
  hence thesis by A1,CQC_THE1:55;
end;
