theorem
  p is closed & X \/ {'not' p} |- 'not' q implies X \/ {q} |- p
proof
  assume that
A1: p is closed and
A2: X \/ {'not' p} |- 'not' q;
  'not' p is closed by A1,QC_LANG3:21;
  then X |- 'not' p => 'not' q by A2,CQC_THE2:92;
  then X |- q => p by LUKASI_1:69;
  hence thesis by Th40;
end;
