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.
malik:2-16Mālik

Yahya related to me from Malik that he saw Rabia ibn Abd ar- Rahman vomit several times when he was in the mosque and he did not leave, nor did he do wudu before he prayed. Yahya said that Malik was asked whether a man who vomited food had to do wudu and he said, "He does not have to do wudu, but he should rinse the inside of his mouth and wash his mouth out."  

مالك:٢-١٦وَحَدَّثَنِي عَنْ مَالِكٍ

أَنَّهُ رَأَى رَبِيعَةَ بْنَ أَبِي عَبْدِ الرَّحْمَنِ يَقْلِسُ مِرَارًا وَهُوَ فِي الْمَسْجِدِ فَلاَ يَنْصَرِفُ وَلاَ يَتَوَضَّأُ حَتَّى يُصَلِّيَ قَالَ يَحْيَى وَسُئِلَ مَالِكٌ عَنْ رَجُلٍ قَلَسَ طَعَامًا هَلْ عَلَيْهِ وُضُوءٌ فَقَالَ لَيْسَ عَلَيْهِ وُضُوءٌ وَلْيَتَمَضْمَضْ مِنْ ذَلِكَ وَلْيَغْسِلْ فَاهُ