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

theorem
  ( ( p => q ) '&' (p => s) ) => ( p => (q '&' s) ) in HP_TAUT
proof
  set P = p => q, Q = p => s, S = p => (q '&' s);
A1: P => (Q => S) in HP_TAUT by Th35;
  ( P => ( Q => S )) => (( P '&' Q ) => S ) in HP_TAUT by Th34;
  hence thesis by A1,Def10;
end;
