Muslim

Hadith Commentary:
Imam Bukhari has brought this hadith as an example of indication (dalalah), in that the Prophet sallallahu alayhi wa sallam understood from the woman’s statement, “I do not find you,” that what she meant was his death.

Some have said that in this there is an indication of Abu Bakr as-Siddiq radi Allahu anhu being the caliph, and as for what Umar radi Allahu anhu said—that the Prophet sallallahu alayhi wa sallam did not appoint anyone as caliph—its meaning is that he did not do so explicitly; otherwise, by way of indication, it is known from several ahadith that the Prophet sallallahu alayhi wa sallam intended that Abu Bakr as-Siddiq radi Allahu anhu should be made caliph.

For example, this hadith, and the hadith in which, during his final illness, the Prophet sallallahu alayhi wa sallam ordered Abu Bakr radi Allahu anhu to lead the prayer (salah), and the hadith of Aisha radi Allahu anha in which she said, “Call my brother and my father, so that I may write (a will), lest someone who desires (leadership) should desire something else,” and the hadith in which the Companions asked the Prophet sallallahu alayhi wa sallam, “Whom should we appoint as caliph after you?” He replied, “If you appoint Abu Bakr radi Allahu anhu, he is such-and-such; if you appoint Umar radi Allahu anhu, he is such-and-such; if you appoint Ali radi Allahu anhu, he is such-and-such, but I do not expect that you will appoint Ali radi Allahu anhu.”

In this hadith as well, Abu Bakr radi Allahu anhu is mentioned first, and Shah Waliullah sahib has discussed this topic in great detail in Izalat al-Khafa.

Hadith Commentary:
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When the Messenger of Allah (sallallahu alayhi wa sallam) told that woman to come again, she said:
“If I do not find you (present), then what should I do?” It is as if by “not finding you,” she meant the death of the Prophet (sallallahu alayhi wa sallam).
(Sahih al-Bukhari, Virtues of the Companions of the Prophet sallallahu alayhi wa sallam, Hadith: 3659)
Imam al-Bukhari rahimahullah has presented this hadith as an example of rational inference, that when she gave this response, the Messenger of Allah (sallallahu alayhi wa sallam) understood from her manner of speaking that by this she meant his death. Therefore, the Prophet (sallallahu alayhi wa sallam) advised her to go to Abu Bakr (radi Allahu anhu).
Although there is no explicit statement here that Abu Bakr al-Siddiq (radi Allahu anhu) would become the caliph,
nevertheless, there is a strong indication and a clear hint. Thus, Imam al-Bukhari rahimahullah has deduced from this hadith the caliphate of Abu Bakr (radi Allahu anhu).
(Sahih al-Bukhari, Book of Rulings, Hadith: 7220)
He has established the heading of “Caliphate” for this hadith.
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The statement of Umar (radi Allahu anhu) that the Messenger of Allah (sallallahu alayhi wa sallam) did not appoint anyone as caliph after him is not contrary to this indication, because by this Umar (radi Allahu anhu) meant “an explicit and clear nomination.” However, there are numerous indications, the explanation of which we have already mentioned in the Book of Rulings.
And Allah knows best.

Hadith Commentary:
This hadith is clear evidence of the fact that the Prophet sallallahu alayhi wa sallam knew that after him, Abu Bakr radi Allahu anhu would be the caliph.
In another narration, which has been recorded by Tabarani and Isma‘ili, it is stated as follows: A Bedouin pledged allegiance to the Prophet sallallahu alayhi wa sallam and asked, “If you pass away, to whom should I go?” He replied, “Go to Abu Bakr radi Allahu anhu.”
He asked, “If he also passes away?” The Prophet said, “Then go to Umar radi Allahu anhu.”
This is clear proof of the training and preparation for the caliphate.

Hadith Commentary:
1.
This hadith is clear evidence that after the Messenger of Allah (sallallahu alayhi wa sallam), the caliphate of Abu Bakr as-Siddiq (radi Allahu anhu) was legitimate, and the Messenger of Allah (sallallahu alayhi wa sallam) knew that after him, Abu Bakr (radi Allahu anhu) would be the caliph. However, in this hadith, there is not an explicit statement but rather a clear indication.
(Fath al-Bari: 13/407)
There is a narration that a Bedouin pledged allegiance to the Messenger of Allah (sallallahu alayhi wa sallam) and asked:
“If you pass away, to whom should I come?” The Prophet (sallallahu alayhi wa sallam) replied:
“Go to Abu Bakr.”
He asked:
“And if he also passes away?” The Prophet (sallallahu alayhi wa sallam) said:
“Then go to Umar (radi Allahu anhu).”
From this as well, the order of the caliphate is understood.
(Fath al-Bari: 7/31)

Hadith Commentary:
From this hadith, it is derived that it had already been revealed to you through revelation (wahy) that after you, Abu Bakr (radi Allahu anhu) would be your successor (khalifah).
Tabarani has narrated from ‘Ismah bin Malik:
We submitted, “O Messenger of Allah (sallallahu alayhi wa sallam)! After you, to whom should we give the zakat of our wealth?” You replied, “Give it to Abu Bakr (radi Allahu anhu).” Its chain of narration is weak. In al-Mu‘jam, it is narrated from Sahl bin Abi Khaythamah that a Bedouin pledged allegiance to you and asked, “If you pass away, to whom should I go?” You replied, “Go to Abu Bakr.”
He said, “If he passes away, then to whom?” You replied, “To ‘Umar (radi Allahu anhu).”
These narrations refute the Shia who claim that the Prophet (sallallahu alayhi wa sallam) appointed ‘Ali (radi Allahu anhu) as his successor after him.

Hadith Commentary:
1.
From this hadith, there is a clear indication of Abu Bakr radi Allahu anhu becoming the caliph after the passing of the Messenger of Allah sallallahu alayhi wa sallam.
When it was said to Umar radi Allahu anhu that he should appoint someone as caliph, he replied:
"The Messenger of Allah sallallahu alayhi wa sallam did not appoint anyone as caliph." His statement is not contrary to the aforementioned narration, because what Umar radi Allahu anhu meant was that the Messenger of Allah sallallahu alayhi wa sallam did not explicitly appoint anyone; this does not contradict the indication (isharah).
However, it is mentioned in Tabarani that the noble Companions radi Allahu anhum ajma'in submitted:
"O Messenger of Allah sallallahu alayhi wa sallam! After you, to whom should we give the charity from our wealth?" So he sallallahu alayhi wa sallam said:
"After me, give your charity to Abu Bakr."
There is some explicitness in this narration, but its chain of transmission is extremely weak.
(Fath al-Bari: 7/31)
2.
This hadith refutes those Shia individuals who claim that the Messenger of Allah sallallahu alayhi wa sallam made a bequest to appoint Ali radi Allahu anhu and Abbas radi Allahu anhu as caliphs.
3.
It should be noted that Imam Bukhari rahimahullah establishes two types of chapter headings: one is of a fundamental nature, as he has established the chapter on the virtue of Abu Bakr radi Allahu anhu for these ahadith. However, sometimes the ahadith presented contain, in addition to the fundamental issue, some additional benefit; therefore, due to the importance of that, he establishes a separate, additional chapter heading. For example, for the previous ahadith, he established a chapter:
(Bab Qawl al-Nabi sallallahu alayhi wa sallam: Law kuntu muttakhidhan khalilan)
"Chapter: The statement of the Prophet sallallahu alayhi wa sallam: If I were to take a close friend (khalil) other than Allah, I would have taken Abu Bakr as a close friend."
This clarification is necessary because the aforementioned hadith presented does not correspond to the additional chapter heading, but rather corresponds to its fundamental chapter heading.
And Allah knows best.

Explanation:
1:
In this, there is a prophecy regarding Abu Bakr radi Allahu anhu being your (sallallahu alayhi wa sallam) successor after you, and an indication to the people about appointing him as your successor.