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

theorem Th32:
  ( p => ( q => r )) => (( p '&' q ) => r ) in TAUT(A)
proof
A1: ( p => (( p '&' q ) => r )) => ((p '&' q ) => ( p => r )) in TAUT(A) by
LUKASI_1:8;
  ((p '&' q ) => ( p => r )) => ((( p '&' q ) => p ) => (( p '&' q ) => r
  )) in TAUT(A) by LUKASI_1:11;
  then
A2: ((p '&' q ) => ( p => r )) => (( p '&' q ) => r ) in TAUT(A) by Th19,
LUKASI_1:16;
  ( p '&' q ) => q in TAUT(A) & (( p '&' q ) => q) => (( q => r ) => (( p '&'
  q ) => r )) in TAUT(A) by Th21,LUKASI_1:1;
  then ( q => r ) => (( p '&' q ) => r ) in TAUT(A) by CQC_THE1:46;
  then
A3: p => (( q => r ) => (( p '&' q ) => r )) in TAUT(A) by LUKASI_1:13;
  p => (( q => r ) => (( p '&' q ) => r )) => ((p => ( q => r )) => ( p =>
  (( p '&' q ) => r ))) in TAUT(A) by LUKASI_1:11;
  then (p => ( q => r )) => ( p => (( p '&' q ) => r )) in TAUT(A) by A3,
CQC_THE1:46;
  then (p => ( q => r )) => ((p '&' q ) => ( p => r )) in TAUT(A)
  by A1,LUKASI_1:3;
  hence thesis by A2,LUKASI_1:3;
end;
