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

theorem
  ( p '&' 'not' q ) => 'not' p in TAUT(A) implies p => q in TAUT(A)
proof
A1: 'not' ( p '&' 'not' q ) = ( p => q ) by QC_LANG2:def 2;
  assume ( p '&' 'not' q ) => 'not' p in TAUT(A);
  then
A2: 'not' 'not' p => 'not' ( p '&' 'not' q ) in TAUT(A) by LUKASI_1:34;
  p => 'not' 'not' p in TAUT(A) by LUKASI_1:27;
  then p => 'not' ( p '&' 'not' q ) in TAUT(A) by A2,LUKASI_1:3;
  hence thesis by A1,LUKASI_1:18;
end;
