Does the intention invalidate the ablution such that it is impermissible to pray Asr with ablution intended for Dhuhr prayer?

If someone performs ablution (Wudu') with the intention of performing a specific prayer, it is permissible for him to perform as many other prayers as he wishes with that same ablution, as long as his ablution has not been invalidated. This is because by removing the state of ritual impurity (hadath), he is permitted to perform all prayers and acts that are otherwise prohibited by hadath, such as touching the Qur'an and circumambulating the Kaaba (Tawaf).