When sending greetings to Prophet Muhammad,

some say: Peace be upon him (PBUH)

others say: Peace be upon him and his family (PBUH&HF)

some others say are more generous and say: Peace be upon him and his family (Aalihi) and his wives (wa Azwajihi) and all his companions (wa Sahbihi Ajma'een).

Now let us see how the Prophet himself thought us to send blessing for him:

The Messenger of Allah (PBUH&HF) said, "Do not salute for me in short!" The companions asked, "What is saluting in short?" The Prophet replied, "Saying that Blessing of Allah be upon Muhammad." They asked, "what should we say?" the Prophet (PBUH&HF) answered, "Say: Blessing of Allah be upon Muhammad and his Ahlul-Bayt." In another wordings the Prophet replied: "Say: O Allah bless Muhammad and his household the same way as you blessed Abraham and his household. Verily you are worthy of all praise full of all glory!".

Sunni reference:

al-Sawa'iq al-Muhriqah, by Ibn Hajar, Ch. 11, section 1, p225

This saying of the Prophet was in connection with the following verse of Quran which was related about the House of Abraham (AS):

They said: "Do you wonder at Allah's decree? The Mercy of Allah and His Blessings be upon you O people of the house! for He is indeed worthy of all praise full of all glory!" (Quran 11:73)

قَالُوا أَتَعْجَبِينَ مِنْ أَمْرِ اللَّهِ رَحْمَتُ اللَّهِ وَبَرَكَاتُهُ عَلَيكُمْ أَهْلَ الْبَيتِ إِنَّهُ حَمِيدٌ مَجِيدٌ(هود/73)

Moreover, Ibn Hajar also mentioned that some of the Sunni commentators of Quran have narrated from Ibn Abbas (RA) that the Quranic verse "Peace be upon the family of Yaaseen (Quran 37:130)" refers to the family of Muhammad. (See al-Sawa'iq al-Muhriqah, by Ibn Hajar, Ch. 11, section 1, p228).

From the tradition given earlier, one can see that the Messenger of Allah (PBUH&HF) mentioned his name and his Ahlul-Bayt together, and disliked mentioning his name alone. He specifically ordered that his followers SHOULD include his family in all their greetings to the Prophet Muhammad. This because ONLY those individuals whom Quran testifies to their perfect purity (the last sentence of Verse 33:33) are worthy of being saluted. Let us look at more traditions, this time from Sahih al-Bukhari:

Sahih al-Bukhari Hadith: 6.320

Narrated Ka'b bin Ujra:

It was said, "O Allah's Apostle! We know how to greet you, but how to invoke Allah for you?" The Prophet said, "Say: O Allah! Send your blessings/greetings (Salawat) on Muhammad and his family, the same way as You sent Your blessings/greetings on Abraham's family. You are indeed worthy of all praise, full of glory.'"

Sahih al-Bukhari Hadith: 6.321

Narrated Abu Said al-Khudri:

We said, "O Allah's Apostle! (We know) this greeting (to you) but how shall we invoke Allah for you?" He said, "Say: O Allah! Send your greetings on Muhammad who is Your servant and Your Messenger, the same way as You sent Your greetings on Abraham's family. And send Your blessings on Muhammad and on Muhammad's family, the same way as You sent Your blessings on Abraham's family."

Sahih al-Bukhari Hadith: 6.322

Narrated Ibn Abi Hazim and Ad-Darawardi:

Yazid reported (similarly with the following wordings) "...And send Your blessings on Muhammad and on Muhammad's family, the same way as You sent Your blessings on Abraham and on Abraham's family."

Sahih al-Bukhari Hadith: 8.368

Narrated 'Abdur-Rahman bin Abi Laila:

Ka'b bin 'Ujra met me and said, "Shall I give you a present? Once the Prophet (saw) came to us and we said, 'O Allah's Apostle! We know how to greet You; but how to send Salat upon you?' He said 'Say: O Allah! Send your greetings (Salawat) on Muhammad and his family, the same way as You sent Your Salawat on Abraham's family. O Allah! Send Your blessings on Muhammad and on Muhammad's family, the same way as You sent Your blessings on Abraham's family. You are indeed worthy of all praise, full of glory.'"

Two more traditions are as follows:

Abu Masud Badri relates: (Once) we, were sitting with Sad bin Ubadah when the Holy Prophet came to us. Bashir Ibn Sad asked the Holy Prophet: O Messenger of Allah, we have been commanded by Allah to invoke blessings on you by reciting Salat, then how shall we do this ? The Holy Prophet kept quite for sometime, so much so that we wished that Bashar bin Sad had not asked the question from the Holy Prophet. After some time the Holy Prophet said these words :

O Allah, send Thy blessings on Muhammad and on the children of Muhammad as Thou didst send Thy blessings on Abraham, and bless Muhammad and the children of Muhammad as Thou didst bless Abraham. Indeed Thou art the praiseworthy, the Glorious. Continuing, the Holy Prophet said : and the salutation is already known to you.

Sunni reference: Riyadh al-Saliheen, by al-Nawawi, English version, Tradition #1406

Although the above traditions confirm that the Prophet (PBUH&HF) ordered people to send Salawat on him and his family. This can not be regarded as self-esteem, rather it was the order by Allah to do that. It served as teaching the Sunnah to people. Specially the highlighted part in the last tradition shows that the Prophet was hesitating to salute himself at first, but since it was the order of Allah, he conveyed the message. In another tradition:

When the Messenger of Allah noticed that a blessing from Allah was to descent, he told Safiyya (one of his wives): "Call for me! Call for me!" Safiyya said: "Call who, O the Messenger of Allah?" He said: "Call for me my Ahlul-Bayt who are Ali, Fatimah, al-Hasan, and al-Husain." Thus we sent for them and they came to him. Then the Prophet (PBUH&HF) spread his cloak (upper garment) over them, and raised his hand (toward sky) saying: "O Allah! These are my family (Aalee), so bless Muhammad and the family (Aal) of Muhammad." And Allah, to whom belong Might and Majesty, revealed: "Verily Allah intends to keep off from you every kind of uncleanness O' People of the House (Ahlul-Bayt), and purify you a thorough purification (Quran, the last sentence of Verse 33:33)".

Sunni references:

al-Mustadrak by al-Hakim, Chapter of "Understanding (the virtues) of Companions, v3, p148. The author then wrote: "This tradition is authentic (Sahih) based on the criteria of the two Shaikhs (al-Bukhari and Muslim)."

Talkhis of al-Mustadrak, by al-Dhahabi, v3, p148

Usdul Ghabah, v3, p33

Similarly, it is narrated that in another occasion, when the Messenger of Allah gathered Ali, Fatimah, al-Hasan, al-Husain (peace be upon them all) under his cloak, he said:

"O Allah! Verily they are from me and I am from them. Thus place Your blessings and Your mercy and Your satisfaction on me and them."

and:

"O Allah! These are Aale-Muhammad (family of Muhammad). Thus place Your blessings and Your bounty upon the family of Muhammad, for, indeed You are the praiseworthy, the Glorious."

Sunni reference:

al-Sawa'iq al-Muhriqah, by Ibn Hajar, Ch. 11, section 1, p225, quoted from Ahmad Ibn Hanbal

Also it is narrated that:

The Messenger of Allah (PBUH&HF) said: "If one prays, and in it he does not send blessings to me and my family, his prayer will not be accepted."

Sunni references:

al-Darqunti, and al-Bayhaqi, as quoted in:

al-Sawa'iq al-Muhriqah, by Ibn Hajar al-Haythami, Ch. 11, p349

In fact, invoking Salawat on the Prophet's family was so important that it has been included in ANY Salawat on the Prophet (PBUH&HF). Invoking Salawat on the family of the Prophet is a sign of pledging allegiance to them, and affirming what Allah Himself has affirmed for them: They are perfectly cleansed and worthy of being saluted.

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Side Comment

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Earlier, a Sunni brother mentioned that

I thought that "SWS" and "AS" were used for the prophets whereas "RA" was used for others including Ali (RA)

The abbreviation "AS" stands for "Alayhi-s-Salam" meaning "peace be upon him". I am interested to know from where you concluded that we can not use this term for a non-prophet? Could you quote a verse from Quran or an authentic tradition that we can not use the phrase "Peace be upon him" after his (AS) name?

Dear brother, if we want to follow the Sunnah of Prophet (PBUH&HF), we are ORDERED by the above authentic traditions to send peace not only to Imam Ali (AS) but also to all the members of the House of Prophet. If the Prophet (PBUH&HF) ordered us to send Peace and blessing to his family, then who are we to set regulations in contrary to that and yet claim to follow the Sunnah of Prophet?

The phrase "May Allah be please with him" (RA) can be used for the companions, not for Prophet and his Ahlul-Bayt who are perfectly pure, flawless, and sinless.