reserve T, X, Y for Subset of HP-WFF;
reserve p, q, r, s for Element of HP-WFF;

theorem Th33:
  (( p '&' q ) => r ) => ( p => ( q => r )) in HP_TAUT
proof
  set qp = ( q => ( p '&' q ));
  set pr = (( p '&' q ) => r) => ( q => r );
A1: ( p => ( qp => pr )) => ( ( p => qp ) => ( p => pr )) in HP_TAUT by Def10;
A2: p => ( q => ( p '&' q )) in HP_TAUT by Def10;
  p => (( q => ( p '&' q )) => ((( p '&' q ) => r ) => ( q => r ))) in
  HP_TAUT by Th15,Th21;
  then ( ( p => qp ) => ( p => pr )) in HP_TAUT by A1,Def10;
  then
A3: p => ((( p '&' q ) => r ) => ( q => r )) in HP_TAUT by A2,Def10;
  (p => ((( p '&' q ) => r ) => ( q => r ))) => ((( p '&' q ) => r ) => (
  p => ( q => r ))) in HP_TAUT by Th26;
  hence thesis by A3,Def10;
end;
