The Messenger of Allah ﷺ took a bath and offered two rak'ahs of prayer and said the dawn prayer. I do not think he performed ablution afresh after taking a bath. (Using translation from Abū Dāʾūd 250)
أَنَّ رَسُولَ اللهِ ﷺ كَانَ يَغْتَسِلُ وَيُصَلِّي الرَّكْعَتَيْنِ وَصَلَاةَ الْغَدَاةِ لَا أَرَاهُ يُحْدِثُ وُضُوءًا بَعْدَ الْغُسْلِ