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

theorem Th44:
  ( p => q ) '&' ( p '&' s ) => ( s '&' q ) in HP_TAUT
proof
A1: ( q '&' s ) => ( s '&' q ) in HP_TAUT by Th43;
  ( p => q ) '&' ( p '&' s ) => ( q '&' s ) in HP_TAUT by Th42;
  hence thesis by A1,Th23;
end;
