reserve X,Y for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,h for Function;

theorem
  f = {} implies f" = {}
proof
  assume f = {};
  then dom(f") = {} by FUNCT_1:33,RELAT_1:38;
  hence thesis;
end;
