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

theorem Th40:
  ( (p '&' s) => q ) => ((p '&' s) => (q '&' s)) in HP_TAUT
proof
  set P = p '&' s;
A1: ( P => q ) => (( P => s ) => ( P => ( q '&' s ))) in HP_TAUT by Th35;
  P => s in HP_TAUT by Def10;
  hence thesis by A1,Th29;
end;
