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

theorem Th27:
  ( p 'or' ( q 'or' r )) => (( p 'or' q ) 'or' r ) in TAUT(A)
proof
A1: ( 'not' p => ( 'not' r => q )) => ( 'not' r => ( 'not' p => q )) in TAUT(A)
  by LUKASI_1:8;
  'not' p => (( 'not' q => r ) => ( 'not' r => q )) in TAUT(A) & ( 'not' p =>
(( 'not' q => r ) => ( 'not' r => q ))) => (( 'not' p => ( 'not' q => r )) => (
  'not' p => ( 'not' r => q ))) in TAUT(A) by LUKASI_1:11,13,31;
  then
A2: ( 'not' p => ( 'not' q => r )) => ( 'not' p => ( 'not' r => q )) in TAUT(A)
  by CQC_THE1:46;
  ( p 'or' ( q 'or' r )) => ( 'not' p => ( q 'or' r )) in TAUT(A) by Th5;
  then ( p 'or' ( q 'or' r )) => ( 'not' p => ( 'not' q => r )) in TAUT(A)
  by Lm1;
  then ( p 'or' ( q 'or' r )) => ( 'not' p => ( 'not' r => q )) in TAUT(A)
by A2,LUKASI_1:3;
  then ( p 'or' ( q 'or' r )) => ( 'not' r => ( 'not' p => q )) in TAUT(A)
by A1,LUKASI_1:3;
  then
A3: ( p 'or' ( q 'or' r )) => ( r 'or' ( 'not' p => q )) in TAUT(A) by Lm1;
  ( r 'or' ( 'not' p => q )) => (( 'not' p => q ) 'or' r) in TAUT(A) by Th8;
  then ( p 'or' ( q 'or' r )) => (( 'not' p => q ) 'or' r) in TAUT(A) by A3,
LUKASI_1:3;
  hence thesis by Lm1;
end;
