Sunan Abi Dawud Book 2, Hadith 180

‘Abd Allah (b. Mas’ud) reported the prophet (ﷺ) as saying; it is more excellent for a woman to pray in her house than in her courtyard, and more excellent for her to pray in her private chamber than in her house.

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yes.

Sunan Abi Dawud Book 2, Hadith 179
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if we reserve this door for women (it would be better). Nafi' said: Ibn ‘Umar did not enter through it( the door) till he died.

Abu Dawud said: This tradition has been narrated though a different chain of transmitters by 'Umar. And this is more correct.

Sunan Abi Dawud Book 2, Hadith 181