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

theorem Th19:
  ( p '&' q ) => p in TAUT(A)
proof
  'not' p => ( 'not' p 'or' 'not' q ) in TAUT(A) by Th3;
  then
A1: 'not' ( 'not' p 'or' 'not' q ) => 'not' 'not' p in TAUT(A) by LUKASI_1:34;
  ( 'not' p 'or' 'not' q ) => 'not' ( p '&' q ) in TAUT(A) by Th18;
  then
A2: 'not' 'not' ( p '&' q ) => 'not' ( 'not' p 'or' 'not' q ) in TAUT(A) by
LUKASI_1:34;
  ( p '&' q ) => 'not' 'not' ( p '&' q ) in TAUT(A) by LUKASI_1:27;
  then
A3: ( p '&' q ) => 'not' ( 'not' p 'or' 'not' q ) in TAUT(A) by A2,LUKASI_1:3;
  'not' 'not' p => p in TAUT(A) by LUKASI_1:25;
  then 'not' ( 'not' p 'or' 'not' q ) => p in TAUT(A) by A1,LUKASI_1:3;
  hence thesis by A3,LUKASI_1:3;
end;
