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;
