Caution: Translations of Quran and Ḥadīth may lead to possible misapplications and misinterpretations. This site is intended for students of sacred knowledge that are proficient in comprehending classical Arabic and have a strong foundation in Islamic sciences. Also note that religious injunctions rely on several aspects beyond what one may glean through reading individual aḥādīth.
tirmidhi:295Muḥammad b. Bashhār > ʿAbd al-Raḥman b. Mahdī > Sufyān > Abū Isḥāq > Abū al-Aḥwaṣ > ʿAbdullāh

"The Prophet would say the Salam from his right and from his left (saying): (As-Salamu alaikum wa rahmatullah, as-Salamu alaikum wa rahmatullah) 'Peace be upon you, and Allah's mercy. Peace be upon you, and Allah's mercy.'"  

الترمذي:٢٩٥حَدَّثَنَا مُحَمَّدُ بْنُ بَشَّارٍ حَدَّثَنَا عَبْدُ الرَّحْمَنِ بْنُ مَهْدِيٍّ حَدَّثَنَا سُفْيَانُ عَنْ أَبِي إِسْحَاقَ عَنْ أَبِي الأَحْوَصِ عَنْ عَبْدِ اللَّهِ

عَنِ النَّبِيِّ ﷺ أَنَّهُ كَانَ يُسَلِّمُ عَنْ يَمِينِهِ وَعَنْ يَسَارِهِ السَّلاَمُ عَلَيْكُمْ وَرَحْمَةُ اللَّهِ السَّلاَمُ عَلَيْكُمْ وَرَحْمَةُ اللَّهِ قَالَ وَفِي الْبَابِ عَنْ سَعْدِ بْنِ أَبِي وَقَّاصٍ وَابْنِ عُمَرَ وَجَابِرِ بْنِ سَمُرَةَ وَالْبَرَاءِ وَأَبِي سَعِيدٍ وَعَمَّارٍ وَوَائِلِ بْنِ حُجْرٍ وَعَدِيِّ بْنِ عَمِيرَةَ وَجَابِرِ بْنِ عَبْدِ اللَّهِ  

قَالَ أَبُو عِيسَى حَدِيثُ ابْنِ مَسْعُودٍ حَدِيثٌ حَسَنٌ صَحِيحٌ وَالْعَمَلُ عَلَيْهِ عِنْدَ أَكْثَرِ أَهْلِ الْعِلْمِ مِنْ أَصْحَابِ النَّبِيِّ ﷺ وَمَنْ بَعْدَهُمْ وَهُوَ قَوْلُ سُفْيَانَ الثَّوْرِيِّ وَابْنِ الْمُبَارَكِ وَأَحْمَدَ وَإِسْحَاقَ