reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;

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;
