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

theorem Th28:
  p => ( q => ( p '&' q )) in TAUT(A)
proof
A1: ((( p '&' q ) 'or' 'not' p ) 'or' 'not' q ) => ( 'not' q 'or' (( p '&' q
  ) 'or' 'not' p )) in TAUT(A) by Th8;
  'not' ( p '&' q ) => ( 'not' p 'or' 'not' q ) in TAUT(A) by Th17;
  then
A2: ( p '&' q ) 'or' ( 'not' p 'or' 'not' q ) in TAUT(A) by Lm1;
  ( p '&' q ) 'or' ( 'not' p 'or' 'not' q ) => ((( p '&' q ) 'or' 'not' p
  ) 'or' 'not' q ) in TAUT(A) by Th27;
  then ((( p '&' q ) 'or' 'not' p ) 'or' 'not' q ) in TAUT(A)
   by A2,CQC_THE1:46;
  then ( 'not' q 'or' (( p '&' q ) 'or' 'not' p )) in TAUT(A)
  by A1,CQC_THE1:46;
  then
A3: ( 'not' 'not' q => (( p '&' q ) 'or' 'not' p )) in TAUT(A) by Lm1;
  q => ((( p '&' q ) 'or' 'not' p ) => ( 'not' p 'or' ( p '&' q ))) in
TAUT(A) & (q => ((( p '&' q ) 'or' 'not' p ) => ( 'not' p 'or' ( p '&' q ))))
 => (
  (q => ( p '&' q ) 'or' 'not' p ) => ( q => ( 'not' p 'or' ( p '&' q )))) in
  TAUT(A) by Th8,LUKASI_1:11,13;
  then
A4: (q => ( p '&' q ) 'or' 'not' p ) => ( q => ( 'not' p 'or' ( p '&' q )))
  in TAUT(A) by CQC_THE1:46;
  q => 'not' 'not' q in TAUT(A) by LUKASI_1:27;
  then ( q => (( p '&' q ) 'or' 'not' p )) in TAUT(A) by A3,LUKASI_1:3;
  then ( q => ( 'not' p 'or' ( p '&' q ))) in TAUT(A) by A4,CQC_THE1:46;
  then ( q => ( 'not' 'not' p => ( p '&' q ))) in TAUT(A) by Lm1;
  then
A5: 'not' 'not' p => ( q => ( p '&' q )) in TAUT(A) by LUKASI_1:15;
  p => 'not' 'not' p in TAUT(A) by LUKASI_1:27;
  hence thesis by A5,LUKASI_1:3;
end;
