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

theorem Th35:
  ( r => p ) => (( r => q ) => ( r => ( p '&' q ))) in HP_TAUT
proof
A1: ( r => ( q => ( p '&' q ))) => (( r => q ) => ( r => ( p '&' q ))) in
  HP_TAUT by Def10;
  p => ( q => ( p '&' q )) in HP_TAUT by Def10;
  then
A2: r => ( p => ( q => ( p '&' q ))) in HP_TAUT by Th15;
  (r => ( p => ( q => ( p '&' q )))) => (( r => p ) => ( r => ( q => ( p
  '&' q )))) in HP_TAUT by Def10;
  then ( r => p ) => ( r => ( q => ( p '&' q ))) in HP_TAUT by A2,Def10;
  hence thesis by A1,Th23;
end;
