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 Th43:
  p is closed & p |- q implies 'not' q |- 'not' p
proof
  assume that
A1: p is closed and
A2: p |- q;
  p => q is valid by A1,A2,Th41;
  then 'not' q => 'not' p is valid by LUKASI_1:52;
  hence thesis by Th39;
end;
