Sahih Al Bukhari – Book of Prophets
Volumn 004, Book 055, Hadith Number 609.
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Narated By Ibn 'Abbas RA: When the Prophet PBUH came to Medina, he found (the Jews) fasting on the day of 'Ashura' (i.e. 10th of Muharram). They used to say: "This is a great day on which Allah SWT saved Moses RA and drowned the folk of Pharaoh. Moses RA observed the fast on this day, as a sign of gratitude to Allah SWT." The Prophet PBUH said, "I am closer to Moses RA than they." So, he observed the fast (on that day) and ordered the Muslims to fast on it.