The Prophet ﷺ ate of the meat of a shoulder (by cutting the meat with his teeth), and then got up and offered the prayer without performing the ablution anew.  

تَعَرَّقَ رَسُولُ اللَّهِ ﷺ كَتِفًا ثُمَّ قَامَ فَصَلَّى وَلَمْ يَتَوَضَّأْ  

The Prophet ﷺ took out a bone with meat on it from a cooking pot and ate of it, and then offered the prayer without performing ablution anew.  

انْتَشَلَ النَّبِيُّ ﷺ عَرْقًا مِنْ قِدْرٍ فَأَكَلَ ثُمَّ صَلَّى وَلَمْ يَتَوَضَّأْ