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

theorem
  ( p => ( q '&' 'not' q )) => 'not' p in TAUT(A)
proof
  p => 'not' ( q '&' 'not' q ) in TAUT(A) by Th1,LUKASI_1:13;
  then
A1: 'not' 'not' ( q '&' 'not' q ) => 'not' p in TAUT(A) by LUKASI_1:34;
  ( q '&' 'not' q ) => 'not' 'not' ( q '&' 'not' q ) in TAUT(A) by LUKASI_1:27;
  then ( q '&' 'not' q ) => 'not' p in TAUT(A) by A1,LUKASI_1:3;
  then
A2: p => (( q '&' 'not' q ) => 'not' p) in TAUT(A) by LUKASI_1:13;
  'not' 'not' p => p in TAUT(A) & ( 'not' 'not' p => p ) => (( p => 'not' p
  ) => ( 'not' 'not' p => 'not' p )) in TAUT(A) by LUKASI_1:1,25;
  then
  ( 'not' 'not' p => 'not' p ) => 'not' p in TAUT(A) & ( p => 'not' p ) => (
  'not' 'not' p => 'not' p ) in TAUT(A) by CQC_THE1:42,46;
  then
A3: ( p => 'not' p ) => 'not' p in TAUT(A) by LUKASI_1:3;
  p => (( q '&' 'not' q ) => 'not' p) => (( p => ( q '&' 'not' q )) => ( p
  => 'not' p )) in TAUT(A) by LUKASI_1:11;
  then ( p => ( q '&' 'not' q )) => ( p => 'not' p ) in TAUT(A)
  by A2,CQC_THE1:46;
  hence thesis by A3,LUKASI_1:3;
end;
