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.  

كَانَ رَسُولُ اللَّهِ ﷺ يَغْتَسِلُ وَيُصَلِّي الرَّكْعَتَيْنِ وَصَلاَةَ الْغَدَاةِ وَلاَ أُرَاهُ يُحْدِثُ وُضُوءًا بَعْدَ الْغُسْلِ