Praying wrapped in a single garment is permissible
3 hadith
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Hadith 231
Lady Umm Hani bint Abi Talib (may Allah be pleased with her) says that on the day of the conquest of Makkah, the Noble Prophet (peace and blessings of Allah be upon him) wrapped himself in a single cloth and performed eight units (rak‘ahs) of (Duha) prayer.
Hadith Referenceمختصر صحيح بخاري / 231
Hadith 232
Lady Umm Hani (may Allah be pleased with her) says in this narration that the Prophet (peace and blessings be upon him) on the day of the conquest of Makkah, wrapped himself in a single cloth and performed eight units of prayer. When he finished, I said, "O Messenger of Allah! My mother's son (Sayyidina Ali, may Allah be pleased with him) says that he will kill a man, even though I have granted him protection—the son of Hubayrah, so-and-so." The Messenger of Allah (peace and blessings be upon him) said, "O Umm Hani! Whom you have granted protection, we have also granted protection." Umm Hani says that this (prayer) was the forenoon (Duha) prayer.
Hadith Referenceمختصر صحيح بخاري / 232
Hadith 233
Narrated from Sayyiduna Abu Huraira (may Allah be pleased with him) that a questioner asked the Messenger of Allah (peace and blessings of Allah be upon him) about praying in a single garment, so the Messenger of Allah (peace and blessings of Allah be upon him) said: Does each one of you have two garments?