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

theorem Th40:
  (( p 'or' r ) '&' ( q 'or' r )) => (( p '&' q ) 'or' r ) in TAUT(A)
proof
  (( 'not' p => r ) '&' ( 'not' q => r )) => (( 'not' p 'or' 'not' q ) =>
  r) in TAUT(A) by Th36;
  then (( p 'or' r ) '&' ( 'not' q => r )) => (( 'not' p 'or' 'not' q ) => r)
  in TAUT(A) by Lm1;
  then
A1: (( p 'or' r ) '&' ( q 'or' r )) => (( 'not' p 'or' 'not' q ) => r) in
  TAUT(A) by Lm1;
  'not' ( p '&' q ) => ( 'not' p 'or' 'not' q ) in TAUT(A) & ( 'not' ( p '&'
q ) => ( 'not' p 'or' 'not' q )) => ((( 'not' p 'or' 'not' q ) => r) => ( 'not'
  ( p '&' q ) => r )) in TAUT(A) by Th17,LUKASI_1:1;
  then
  (( 'not' p 'or' 'not' q ) => r) => ( 'not' ( p '&' q ) => r ) in TAUT(A) by
CQC_THE1:46;
  then
  (( p 'or' r ) '&' ( q 'or' r )) => ( 'not' ( p '&' q ) => r ) in TAUT(A)
by A1,LUKASI_1:3;
  hence thesis by Lm1;
end;
