The Prophet ﷺ would not go out on the day of Fitr until he had eaten, and he would not eat on the day of Adha until he had prayed.
حدثنا الحسن بن الصباح البزار البغدادي حدثنا عبد الصمد بن عبد الوارث عن ثواب بن عتبة
كان النبي ﷺ لا يخرج يوم الفطر حتى يطعم ولا يطعم يوم الأضحى حتى يصلي
[Its isnad is hasan] Ibn Majah also narrated it in the Book of Fasting, chapter on eating on the day of Eid al-Fitr before going out, 1/hadith 1756, from the hadith of Thawwab, through him, and Ibn Khuzayma graded it sahih, hadith 1426, as did Ibn Hibban, hadith 593, and Hakim, 1/294, and Dhahabi and others.On this subject there is also a report from Ali [mentioned earlier at 530] and Anas [coming up at 543].