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

theorem Th45:
  ( p => q ) => (( p '&' s ) => ( s '&' q )) in HP_TAUT
proof
  set P = p => q, Q = p '&' s, S = s '&' q;
A1: P '&' Q => S in HP_TAUT by Th44;
  (( P '&' Q ) => S ) => ( P => ( Q => S )) in HP_TAUT by Th33;
  hence thesis by A1,Def10;
end;
