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
  ex X,Y st dom ~f c= [:X,Y:]
proof
  now
    let z be object;
    assume z in dom ~f;
    then ex x,y being object st z = [y,x] & [x,y] in dom f by Def2;
    hence ex x,y being object st z = [x,y];
  end;
  hence thesis by Th1;
end;
