It is from the Sunnah that when the muadhin says in the dawn call to prayer, "Hayya ala al-falah," he then says, "Prayer is better than sleep, prayer is better than sleep."
من السنة إذا قال المؤذن في أذان الفجر حي على الفلاح قال: الصلاة خير من النوم، الصلاة خيرم من النوم.
Daraqutni (1/243) narrated it, and Bayhaqi (1/423) narrated it through his route, from Husayn bin Ismail, who said, Muhammad bin Uthman bin Karama narrated to us, Abu Usama narrated to us, Ibn Awn narrated to us, from Muhammad (Ibn Sirin), from Anas, and he mentioned it. Bayhaqi said, "A group likewise narrated it from Abu Usama, and this is a sahih chain." I say, Ibn Khuzayma (386) also narrated it through the route of Muhammad bin Uthman Ajli, from Abu Usama, mentioning something similar.Anas's statement, "It is from the sunnah," means from the sunnah of Muhammad ﷺ, and its ruling is that of a marfu narration, as is established in the sciences of hadith.On this subject there is also what was narrated from Hafs bin Umar bin Saad the muezzin, that Saad used to give the adhan in the masjid of the Messenger of Allah ﷺ. Hafs said, my family told me that Bilal came to the Messenger of Allah ﷺ to call him to the Fajr prayer, and they said, "He is sleeping." So Bilal called out at the top of his voice, "The prayer is better than sleep," and this phrase was then confirmed as part of the Fajr adhan.Darimi (1228) and Tabarani in Mujam al-Kabir (6/40) both narrated this from the hadith of Zuhri, from Hafs bin Umar, mentioning it. Hafs bin Umar was not deemed reliable by anyone except Ibn Hibban, so he is acceptable, meaning if his narration is corroborated by another.This has also been narrated from Abdullah bin Zayd, the man of the adhan, as well as from Ibn Umar, Ayesha, Abu Hurairah, Abdullah bin Busr, and Nuaym bin Nahham, but in all of these there is some discussion.As for what was narrated from Ibn Umar regarding his disapproval of tathwib, this refers to something that people later introduced, as Ishaq said, namely that when the muezzin gives the adhan and the people are slow to come, he says, between the adhan and the iqamah, "The prayer has begun, come to prayer, come to success." This is what Ibn Umar disapproved of, as was narrated by Mujahid, who said, I entered a masjid with Abdullah bin Umar where the adhan had already been called, and we intended to pray there, but the muezzin performed tathwib, so Abdullah bin Umar left the masjid and said, "Take us out from this innovator," and he did not pray there.As for himself, he used to say during the Fajr prayer, "The prayer is better than sleep," and this form of tathwib was the one chosen and approved by the people of knowledge. See Sunan Tirmidhi (1/380–382).As for the listener's response, "You have spoken truly and rightly," it has no basis. See Talkhis Habir (1/211) and Subul Salam (2/65).