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

theorem
  ( p 'or' q ) in TAUT(A) & 'not' q in TAUT(A) implies p in TAUT(A)
proof
  assume that
A1: ( p 'or' q ) in TAUT(A) and
A2: 'not' q in TAUT(A);
  ( q 'or' p ) => ( 'not' q => p ) in TAUT(A) & ( p 'or' q ) => ( q 'or' p )
  in TAUT(A) by Th5,Th8;
  then ( p 'or' q ) => ( 'not' q => p ) in TAUT(A) by LUKASI_1:3;
  then 'not' q => p in TAUT(A) by A1,CQC_THE1:46;
  hence thesis by A2,CQC_THE1:46;
end;
