We see this proven in the layers of change that occur in the tradition, as it is narrated sometimes as saying that this day was the Jewish fast day, on the tenth of the "Sacred" (Muharram) month, when the Jewish people were saved "from Pharaoh" (Sahih Al-Bukhari, Hadith 6.202), and other times simply as "from their enemy" (3.222). It is clear that the reporter of the "from Pharaoh" versions, has simply misunderstood "their enemy" to refer to the external enemy in the Exodus story. In reality, this Hadith has its origin in Jewish Midrashic sources. An excellent compilation of these stories can be found in Louis Ginsberg's, The Legends of the Jews.
In Judaism, Midrash teaches that, "The Day on which God showed Himself merciful to Moses and to his people, was the 10th day of Tishri [Yom Kippur]. This was the day on which Moses was to receive the tables of Law from God for the second time... and all Israel spent it amid prayer and fasting. 'My children, I swear by My Lofty Name that your tears shall be tears of rejoicing for you; this day shall be a day of pardom, of forgiveness, and of cancelling of sins for you, for your children, and your children's children to the end of all generations.'"