[Abu 'Eisa said:] This Hadith is Hasan Sahih. Some of Az-Zuhri's companions did not mention "from Hamzah" in it, they only said: "from Salim, from his father from the Prophet (SAW)." [Malik bin Anas reported this Hadith from Az-Zuhri and he said: "from Salim and Hamzah the sons of 'Abdullah bin 'Umar from their father].
This is how Ibn Abi 'Umar reported this Hadith for us (And he mentioned the chain again).

(Another chain) from Salim, from his father from the Prophet (SAW), but Sa'eed bin 'Abdur-Rahman did not mention "from Hamzah" in it and Sa'eed's narration is more correct because 'Ali bin Al-Madani and Al-Humaidi reported it from Sufyan, [from Az-Zuhri, from Salim and they mentioned that Sufyan said:] "Az-Zuhri did not report this Hadith to us except from Salim from Ibn 'Umar."
Malik bin Anas reported this Hadith from Az-Zuhri and he said: "From Salim and Hamzah, the sons of 'Abdullah bin 'Umar, from their father."
There are narrations on this topic from Sahl bin Sa'd, 'Aishah, and Anas. It has been related that the Prophet (SAW) said: "If there was an omen in anything it would be in a woman, a (riding) beast, and a dwelling."
And it has been reported from Hakim bin Mu'awiyah who said: "I heard the Prophet (SAW) saying: 'There are no omens, but there is a sense of security in a home, a woman, and a horse.'"
(A chain) with that narration.