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 Th29:
  (p => 'not' 'not' q) => (p => q) in TAUT(A) & (p => q) => (p =>
  'not' 'not' q) in TAUT(A)
proof
  (p => ('not' 'not' q => q)) => ((p => 'not' 'not' q) => (p => q)) in
  TAUT(A) & p => ('not' 'not' q => q) in TAUT(A) by Th11,Th13,Th25;
  hence (p => 'not' 'not' q) => (p => q) in TAUT(A) by CQC_THE1:46;
  (p => (q => 'not' 'not' q)) => ((p => q) => (p => 'not' 'not' q)) in
  TAUT(A) & p => (q => 'not' 'not' q) in TAUT(A) by Th11,Th13,Th27;
  hence thesis by CQC_THE1:46;
end;
