The benefits of the hadith: (The Messenger of Allah (peace and blessings be upon him) used to pray on his mount...) and all of its narrations.
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The Shaykh : The summary of these hadiths, most of which are from 'Abdullah ibn 'Umar (may Allah be pleased with them both), is that it is permissible for a person, if he is traveling, to pray on his mount. But does he pray if he is not riding? The scholars differed on this. Some said he does not pray, because that was only reported regarding the mount, and it is known that the one on the mount does not need to do much work, because he is sitting. Others said it is permissible by analogy to riding on the mount. However, the view that it is not permissible is closer to the truth, unless a Sunnah is established for it, but it was not established. Accordingly, we say that the Sunnah was only reported for when one is on the mount. As for when he is walking, he does not pray, and it is sufficient for him that if it is his habit to pray these voluntary prayers, they are recorded for him, based on the saying of the Prophet (peace and blessings be upon him): Yes.
