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 => q) in TAUT(A) iff (p => 'not' 'not' q) in TAUT(A)
proof
  thus (p => q) in TAUT(A) implies (p => 'not' 'not' q) in TAUT(A)
  proof
    assume
A1: p => q in TAUT(A);
    (p => q) => (p => 'not' 'not' q) in TAUT(A) by Th29;
    hence thesis by A1,CQC_THE1:46;
  end;
  assume
A2: p => 'not' 'not' q in TAUT(A);
  (p => 'not' 'not' q) => (p => q) in TAUT(A) by Th29;
  hence thesis by A2,CQC_THE1:46;
end;
