A'isha Radi allaho anha reported: Allah's Messenger (may peace be upon him) was lying in the bed in my apartment with his thigh or his shank uncovered that Abu Bakr sought permission to get in. It was given to him and he conversed in the same very state (the Prophet's thigh or shank uncovered). Then 'Umar sought permission for getting in and it was given to him and he conversed in that very state. Then 'Uthman sought permission for getting in; Allah's Messenger (may peace be upon him) sat down and he set right his clothes. He ('Uthman) then entered and conversed and as he went out, A'isha Radi allaho anha said: Abu Bakr entered and you did not stir and did not observe much care (in arranging your clothes), then 'Umar entered and you did not stir and did not arrange your clothes, then 'Uthman entered and you got up and set your clothes right, thereupon he said: Should I not show modesty to one whom even the Angels show modesty.
Sahih Muslim Book 031, Number 5906:
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"There are more than 70 branches of Iman (Faith). The foremost is the declaration that there is no God except Allah and the least of it is removing harmful things from the path. And Hayaa(shyness) is a branch of Iman.” [Bukhari, Muslim].
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Narrated Abdullah ibn Umar (ra): The Prophet (saws) passed by a man who was admonishing his brother regarding Haya and was saying, "You are very shy, and I am afraid that might harm you." On that, Allah's Apostle said, "Leave him, for Haya is (a part) of Faith." (Bukhari)