reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;

theorem
  for f being PartFunc of {x},Y holds f.:P c= {f.x}
proof
  let f be PartFunc of {x},Y;
  f.:P c= rng f & rng f c= {f.x} by Th16,RELAT_1:111;
  hence thesis;
end;
