What is the ruling on the Dhuhr prayer for a traveler who intended to return on the same day, but arrived at dawn and prayed Dhuhr before departing to return?

A traveler is permitted to break their fast in Ramadan if the distance is long, and they must make up for that day, according to the Almighty's saying: "But whoever is ill or on a journey, then [he must fast] an equal number of other days."