The Prophet ﷺ would not go out on the day of Eid al-Fitr until he had eaten, and he would not eat on the day of Eid al-Adha until he had prayed.
كان النبي ﷺ لا يخرج يوم الفطر حتى يطعم، ولا يطعم يوم الأضحى حتى يصلي.
Tirmidhi (542), Ibn Majah (1756), Ibn Khuzayma (1426), Ibn Hibban (2812), and Hakim (1/294) all narrated it through the route of Thawab bin Utba Mahri, from Abdullah bin Burayda, from his father, and he related it. The wording given is that of Tirmidhi. The wording of Ibn Majah and Hakim is, "until he returns." The wording of Ibn Khuzayma and Ibn Hibban is, "until he sacrifices." Hakim said, "This is a hadith with a sahih chain that they (Bukhari and Muslim) did not include. Thawab bin Utba Mahri has few narrations, and he was not criticized in any way that would invalidate his hadith. This is a rare practice in terms of narration routes, though it is widespread in the lands of the Muslims."Its chain is hasan due to Thawab bin Utba Mahri, since there is disagreement about him, but he has been corroborated. Imam Ahmad (22984) narrated it from Yunus, who said, Uqba bin Abdullah Rifai told us, he said, Abdullah bin Burayda told me, from his father, who said, "The Messenger of Allah 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 returned, and then he would eat from his udhiya."Bayhaqi (3/283) narrated it through another route, from Ibn Mahdi, from Uqba bin Asamm, from Ibn Burayda, from his father, with an addition, "And when he returned, he would eat from the liver of his udhiya." Uqba bin Asamm is Uqba bin Abdullah Asamm Rifai, who is daif. He was declared daif by Ibn Main, Abu Hatim, Abu Dawud, Nasai, and others. Ibn Adi said, "Some of his hadiths are sound, and some of them are not corroborated."I say, his statement, "And when he returned, he would eat from the liver of his udhiya," is among what is not corroborated. The remarks of some scholars concerning eating the liver should be understood as meaning that it cooks faster and is lighter on the stomach, not that it is recommended in itself.As for someone who eats on the day of sacrifice before offering the udhiya, there is no harm in that, as in the following hadith.