reserve A for QC-alphabet;
reserve p, q, r, s for Element of CQC-WFF(A);

theorem
  p => p '&' p in TAUT(A)
proof
  'not' ( p '&' p ) => ( 'not' p 'or' 'not' p ) in TAUT(A) & ( 'not' p 'or'
  'not' p ) => 'not' p in TAUT(A) by Th11,Th17;
  then 'not' ( p '&' p ) => 'not' p in TAUT(A) by LUKASI_1:3;
  hence thesis by LUKASI_1:35;
end;
