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

theorem Th15:
  ( p '&' q ) => 'not' ( p => 'not' q ) in TAUT(A)
proof
A1: ( p '&' 'not' 'not' q ) => 'not' 'not' ( p '&' 'not' 'not' q ) in TAUT(A)
  by LUKASI_1:27;
  q '&' p => 'not' 'not' q '&' p in TAUT(A) &
  p '&' q => q '&' p in TAUT(A) by Lm2,CQC_THE1:45;
  then
A2: p '&' q => 'not' 'not' q '&' p in TAUT(A) by LUKASI_1:3;
  'not' 'not' q '&' p => p '&' 'not' 'not' q in TAUT(A) by CQC_THE1:45;
  then ( p '&' q ) => ( p '&' 'not' 'not' q ) in TAUT(A) by A2,LUKASI_1:3;
  then ( p '&' q ) => 'not' 'not' ( p '&' 'not' 'not' q ) in TAUT(A) by A1,
LUKASI_1:3;
  hence thesis by QC_LANG2:def 2;
end;
