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

theorem Th41:
  ( p => q ) => ((p '&' s) => (q '&' s)) in HP_TAUT
proof
A1: ( (p '&' s) => q ) => ((p '&' s) => (q '&' s)) in HP_TAUT by Th40;
  (p => q) => (( p '&' s ) => q) in HP_TAUT by Th39;
  hence thesis by A1,Th23;
end;
