This is what Abu Huraira transmitted to us from Muhammad, the Messenger of Allah ﷺ, and he mentioned a number of a hadith, of which this is one: that the Messenger of Allah ﷺ said: When anyone amongst you (performs ablution) he must snuff his nostrils with water and then clean them.
عَنْ مُحَمَّدٍ رَسُولِ اللَّهِ ﷺ فَذَكَرَ أَحَادِيثَ مِنْهَا وَقَالَ رَسُولُ اللَّهِ ﷺ إِذَا تَوَضَّأَ أَحَدُكُمْ فَلْيَسْتَنْشِقْ بِمَنْخِرَيْهِ مِنَ الْمَاءِ ثُمَّ لْيَنْتَثِرْ