reserve A for QC-alphabet;
reserve p, q, r, s, p1, q1 for Element of CQC-WFF(A),
  X, Y, Z, X1, X2 for Subset of CQC-WFF(A),
  h for QC-formula of A,
  x, y for bound_QC-variable of A,
  n for Element of NAT;

theorem Th39:
  p => q is valid implies p |- q
proof
  assume p => q is valid;
  then {p} |- p => q by CQC_THE1:59;
  then {p} |- q by CQC_THE1:55,CQC_THE2:87;
  hence thesis;
end;
