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
  p in TAUT(A) iff 'not' 'not' p in TAUT(A)
proof
  thus p in TAUT(A) implies 'not' 'not' p in TAUT(A)
  proof
    assume
A1: p in TAUT(A);
    p => 'not' 'not' p in TAUT(A) by Th27;
    hence thesis by A1,CQC_THE1:46;
  end;
  assume
A2: 'not' 'not' p in TAUT(A);
  'not' 'not' p => p in TAUT(A) by Th25;
  hence thesis by A2,CQC_THE1:46;
end;
