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

theorem Th42:
  ( p => q ) '&' ( p '&' s ) => ( q '&' s ) in HP_TAUT
proof
  set P = p => q, Q = p '&' s, S = q '&' s;
A1: P => (Q => S) in HP_TAUT by Th41;
  ( P => ( Q => S )) => (( P '&' Q ) => S ) in HP_TAUT by Th34;
  hence thesis by A1,Def10;
end;
