Yes. Predestination, as regards its objects, is a part of providence because the direction of a rational creature towards the end of life eternal is called predestination: to destine, is to direct or send, but the reason of that direction pre-exists in God, as in Him is the type of the order of all things towards an end.
Irrational creatures are not capable of that end which exceeds the faculty of human nature. Whence they cannot be properly said to be predestined; although improperly the term is used in respect of any other end.