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|- 'not' 'not' p iff X|- p
proof
  thus X|- 'not' 'not' p implies X|- p
  proof
    assume
A1: X|- 'not' 'not' p;
    X|- 'not' 'not' p => p by CQC_THE1:59;
    hence thesis by A1,CQC_THE1:55;
  end;
  assume
A2: X|- p;
  X|- p => 'not' 'not' p by CQC_THE1:59;
  hence thesis by A2,CQC_THE1:55;
end;
