Hadith: The Messenger (may Allah's peace and blessings be upon him) prayed on the Day of An-Nahr, then delivered a sermon, then slaughtered (an animal) and said: Whoever slaughtered before praying should slaughter another animal instead, and whoever has not yet slaughtered should slaughter while mentioning Allah's name

عن جُنْدُب بن عَبْدِ الله البجَليِّ رضي الله عنه قال: «صلى النبي صلى الله عليه وسلم يوم النَّحر، ثم خطب، ثم ذبح، وقال: من ذبح قبل أن يُصَلِّيَ فَلْيَذْبَحْ أُخرى مكانها، ومن لم يذبح فَلْيَذْبَحْ باسم الله».
[صحيح] - [متفق عليه]

Jundub ibn ‘Abdullāh al-Bajali (may Allah be pleased with him) reported that the Messenger (may Allah's peace and blessings be upon him) prayed on the Day of Nahr, then delivered a sermon, then slaughtered (an animal) and said: "Whoever slaughtered before praying should slaughter another animal instead, and whoever has not yet slaughtered should slaughter while mentioning Allah's name."
Sahih/Authentic. - [Al-Bukhari and Muslim]

Explanation

The Prophet (may Allah's peace and blessings be upon him) began the Day of An-Nahr with prayer, then delivered the sermon, and then slaughtered. He used to bring and slaughter the animal in the area of Eid prayer; in order to demonstrate the rituals of Islam, as well as to teach Muslims this ritual. He taught them a condition and a ruling of slaughtering: The one who slaughtered before praying Eid prayer should slaughter another one instead, because the first one was not valid; and whoever has not yet slaughtered should do so while mentioning the name of Allah, so that slaughtering be valid and the slaughtered animal becomes permissible to eat. This Hadīth proves the validity of only this order of these rituals. This Hadīth indicates that the slaughtering time starts after the Eid prayer is concluded; neither by the time of the prayer, nor by slaughtering of the Imām, except the one who is exempted from the Eid prayer, i.e. a traveler.