theorem Th45:
  p is closed & 'not' p |- 'not' q implies q |- p
proof
  assume that
A1: p is closed and
A2: 'not' p |- 'not' q;
  'not' p is closed by A1,QC_LANG3:21;
  then 'not' p => 'not' q is valid by A2,Th41;
  then q => p is valid by LUKASI_1:52;
  hence thesis by Th39;
end;
