uniqueness of centre of gravity

An object cannot have two centre of gravity  . This is called  the uniqueness of  centre of gravity. Let us suppose an object has two centre gravity G and G' now as per the definition of centre of gravity at  any posture of the object the gravity force will act  through the point G and G' . On the other hand gravity always acts vertically downwards .so GG' will be always vertical line.  For any posture of the object GG' should be vertical that cannot be possible .  so an object cannot have two centre of gravity . It is an unique point for an object.