Hadithcore
Sahih Muslim, 54 a
sahih

Abu Huraira reported:

The Messenger of Allah (may peace and blessing be upon him) observed: You shall not enter Paradise so long as you do not affirm belief (in all those things which are the articles of faith) and you will not believe as long as you do not love one another. Should I not direct you to a thing which, if you do, will foster love amongst you: (i. e.) give currency to (the practice of paying salutation to one another by saying) as-salamu alaikum.

حَدَّثَنَا أَبُو بَكْرِ بْنُ أَبِي شَيْبَةَ، حَدَّثَنَا أَبُو مُعَاوِيَةَ، وَوَكِيعٌ، عَنِ الأَعْمَشِ، عَنْ أَبِي صَالِحٍ، عَنْ أَبِي هُرَيْرَةَ، قَالَ قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم ‏

‏ لاَ تَدْخُلُونَ الْجَنَّةَ حَتَّى تُؤْمِنُوا وَلاَ تُؤْمِنُوا حَتَّى تَحَابُّوا ‏.‏ أَوَلاَ أَدُلُّكُمْ عَلَى شَىْءٍ إِذَا فَعَلْتُمُوهُ تَحَابَبْتُمْ أَفْشُوا السَّلاَمَ بَيْنَكُمْ ‏

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References2 variants
In-Book Reference
Book 1, Hadith 101
USC-MSA web (English) reference
Book 1, Hadith 96 (deprecated numbering scheme)
Sharh · explanationclick to expand
The Prophet ﷺ used to teach his companions and nation the virtues of righteous deeds that display a feeling of affection among them and raise their ranks in the Hereafter. He also warned us against reasons for hatred and disharmony. Spreading the greetings of peace is one of the causes of love and harmony among Muslims. In this hadith, the Messenger of Allah ﷺ clarified that only believers will enter Paradise and added that love among believers is part of the perfect faith. He said, "You will not enter Paradise until you believe." He means that our faith is neither complete nor benefits us until we love one another. Then he guides us to the best attributes for getting that kind of love in Muslim society which is to declare, act upon, and spread peace among Muslims. Peace is the greeting that Allah, the Almighty, has prescribed for His servants. Once a Muslim passes by another Muslim, relative or stranger, he greets him with peace. Allah made spreading peace a reason for love and affection among Muslims, which is a reason for getting a perfect faith and prevailing the word of Islam. On the other hand, hatred and conflict are reasons for spreading division among Muslims. The form of that greeting as in the narration of Abu Daoud and others is to say, “Peace, mercy, and blessings of Allah be upon you.” Finally, this hadith contains the following benefits such as: (1) The command to spread the greeting of peace among Muslims, for it spreads love and safety among them and (2) It is proof that love is a reason for the perfect faith..
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