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
  'not' 'not' p is valid iff p is valid
proof
  thus 'not' 'not' p is valid implies p is valid
  proof
    assume
A1: 'not' 'not' p is valid;
    'not' 'not' p => p is valid;
    hence thesis by A1,CQC_THE1:65;
  end;
  assume
A2: p is valid;
  p => 'not' 'not' p is valid;
  hence thesis by A2,CQC_THE1:65;
end;
