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

theorem Th18:
  ( 'not' p 'or' 'not' q ) => 'not' ( p '&' q ) in TAUT(A)
proof
A1: ( p => 'not' 'not' p ) => (( 'not' 'not' p => 'not' q ) => ( p => 'not'
  q )) in TAUT(A) by LUKASI_1:1;
  p '&' q => 'not' ( p => 'not' q ) in TAUT(A) by Th15;
  then
A2: 'not' 'not' ( p => 'not' q ) => 'not' ( p '&' q ) in TAUT(A)
by LUKASI_1:34;
  ( p => 'not' q ) => 'not' 'not' ( p => 'not' q ) in TAUT(A) by LUKASI_1:27;
  then
A3: ( p => 'not' q ) => 'not' ( p '&' q ) in TAUT(A) by A2,LUKASI_1:3;
  ( 'not' p 'or' 'not' q ) = ( 'not' 'not' p => 'not' q ) & p => 'not'
  'not' p in TAUT(A) by Lm1,LUKASI_1:27;
  then ( 'not' p 'or' 'not' q ) => ( p => 'not' q ) in TAUT(A)
  by A1,CQC_THE1:46;
  hence thesis by A3,LUKASI_1:3;
end;
