There is no reason to assume that the Hadith is a comprehensive list of those promised paradise. There are literally hundreds of companions who are known to deserve paradise (isA). This Hadith just mentions 10 of them.
Note that the hadith narrated by imam at-Tirmidhi in three versions (here the 3rd, while the 2nd is only a commentary on the first saying that 'Abdurrahman ibn 'Awf narrated it once without quoting his own name -so he quoted only nine sahaba-) appears in sunan ibn Majah, sunan abi Dawod, Musnad Ahmad and many other sources too. The list of sahaba quoted in this ahadith is not final and doesn't exclude other sahaba in fact there are ahadith that suggest other sahaba to be in jannah among them:
Amr ibn al-Jamuh عمرو بن الجموح which has died as shaheed (martyr) in Uhud, as suspected or forseen by our Prophet(), when his sons asked him to stop him from joining the battle as a see in sunan al-Bayhaqi al-Kubra:
كان عمرو بن الجموح أعرج شديد العرج ، وكان له أربعة بنون شباب يغزون مع رسول الله - صلى الله عليه وسلم - إذا غزا ، فلما أراد رسول الله - صلى الله عليه وسلم - يتوجه إلى أحد ، قال له بنوه : إن الله عز وجل قد جعل لك رخصة فلو قعدت فنحن نكفيك ، فقد وضع الله عنك الجهاد ، فأتى عمرو بن الجموح رسول الله - صلى الله عليه وسلم - فقال : يا رسول الله ، إن بني هؤلاء يمنعوني أن أخرج معك ، والله إني لأرجو أن أستشهد ، فأطأ بعرجتي هذه في الجنة ، فقال له رسول الله - صلى الله عليه وسلم : " أما أنت فقد وضع الله عنك الجهاد " ، وقال لبنيه : " وما عليكم أن تدعوه لعل الله عز وجل يرزقه الشهادة ؟ " فخرج مع رسول الله - صلى الله عليه وسلم - فقتل يوم أحد شهيدا .
read also in English:
The extent of his devotion was shown during the Battle of 'Uhud. Amr saw his three sons preparing for the fight. He looked at the three determined young men, fired by the desire for martyrdom, success and the pleasure of Allah the Most High. The scene had a great effect on him and he resolved to go out with them to wage jihad under the banner of the Messenger of Allah, sallallahu 'alayhi wa sallam. The youths, however, were all against their father carrying out his resolve. He was already quite old and extremely weak.
"Father," they said, "surely Allah has excused you. So why do you take this burden on yourself?"
The old man became quite angry and went straight away to the Prophet to complain about his sons. "O Rasulallah! My sons here want to keep me away from this source of goodness, arguing that I am old and decrepit. By Allah, I long to attain Paradise this way even though I am old and infirm." "Let him," said the Prophet to his sons, "Perhaps Allah, the Mighty and the Great, will grant him martyrdom."
Soon it was time to go out to battle. Amr bade farewell to his wife, turned to the qiblah and prayed: "O Lord, grant me martyrdom and don't send me back to my family with my hopes dashed." He set out in the company of his three sons and a large contingent from his tribe, the Banu Salamah. (source)
... أيها الناس إن جعفر بن أبي طالب مع جبريل وميكائيل له جناحان عوضه الله من يديه يطير بهما في الجنة حيث شاء فسلم علي
'Amr ibn Thabit ibn Waqsh (also known as al-Osayrim) الأصيرم عَمْرُو بْنُ ثَابِتِ بْنِ وَقْشٍ the man who entered Jannah on the day he converted to Islam without prostrating even once!
Amr ibn Wqash had given usurious loans in pre-Islamic period; so he disliked to embrace Islam until he took them. He came on the day of Uhud and asked: Where are my cousins? They (the people) replied: At Uhud. He asked: Where is so-and-so? They said: At Uhud. He asked: Where is so-and-so? They said: At Uhud. He then put on his coat of mail and rode his horse; he then proceeded towards them. When the Muslims saw him, they said: Keep away, Amir. He said: I have become a believer. He fought until he was wounded. He was then taken to his family wounded. Sa'd ibn Mu'adh came to his sister: Ask him (whether he fought) out of partisanship, out of anger for them, or out of anger for Allah. He said: Out of anger of Allah and His Apostle. He then died and entered Paradise. He did not offer any prayer for Allah. (sunan abi Dawod and a different narration in Musnad Ahamd)
I heard Allah's Messenger (ﷺ) saying "From among my followers, a group (o 70,000) will enter Paradise without being asked for their accounts, Their faces will be shining like the moon." 'Ukasha bin Muhsin Al-Asadi got up, lifting his covering sheet and said, "O Allah's Messenger (ﷺ) Invoke Allah for me that He may include me with them." The Prophet (ﷺ) said! "O Allah! Make him from them." Then another man from Al-Ansar got up and said, "O Allah's Messenger (ﷺ)! Invoke Allah for me that He may include me with them." On that Allah's Messenger (ﷺ) said, "'Ukasha has anticipated you." (sahih al-Bukhari)
The only difference is that the ten sahaba from the hadith you've quoted have been given the good news at once, not alone or in special circumstances (even if there are ahadith giving them the good news alone or in smaller groups).
So why Bilal has not been included in this hadith is hard to answer and answers on that would be based on assumptions.
Bilal is already in Jannah. The Prophet (SAW) heard his foot steps, therefore Bilal has already entered Jannah. BTW For those ten, it was that nothin could harm their chances of belonging in Jannah. No deed was strong enough to pull them away from the straight path from that day forward. Other people have other ideas, but this is mine. Just a thought
dear these 10 sahabes are called Ashra mubashra .because they were praying with Prophet Muhammad S.W .when prophet were offering prayer the God ordered to divert form Masjed e Aqsa(palestine) towards Masjed e Haram ,these 10 sahabee that were present on that time also followed Porphet. The Hazrat Bilal was not present
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