theorem Th48:
  for f being PartFunc of [:X,Y:],Z holds ~f is PartFunc of [:Y,X:],Z
proof
  let f be PartFunc of [:X,Y:],Z;
A1: dom f c= [:X,Y:];
  then
A2: dom ~f c= [:Y,X:] by Th45;
  rng f c= Z;
  then rng ~f c= Z by A1,Th47;
  hence thesis by A2,RELSET_1:4;
end;
