reserve X,Y,Z,X1,X2,Y1,Y2 for set, x,y,z,t,x1,x2 for object,
  f,g,h,f1,f2,g1,g2 for Function;

theorem
 for x,y being object holds
  [x,y] in dom f implies y in dom curry' f
proof let x,y be object;
 assume [x,y] in dom f;
  then [y,x] in dom ~f by FUNCT_4:42;
  then y in dom curry' f by Th12;
 hence thesis;
end;
