Siman 95 — Fish and Eggs Cooked in a Meat Pot (Noten Taam bar Noten Taam)

According to the Shulchan Aruch (YD 95:1), fish cooked or roasted in a well-washed meat pot, with no fat stuck to it, is permitted to eat with dairy (כותח), because it is a taste of a permitted taste (נותן טעם בר נותן טעם דהיתרא): the taste of meat, already faint, passed into the pot and then into the fish while remaining a permitted taste at every stage. But the Rama (הגה) reports that some are stringent lechatchila in roasting and cooking (יש מחמירין בצלייה ובישול), so that the Ashkenazi custom is to forbid lechatchila and permit bedieved. For practical halacha, consult your Rav.

This is the heart of the siman: a permitted taste (דהיתרא) that is transmitted twice — from the meat to the pot, then from the pot to the fish — remains permitted, because the taste is קלוש (faint) and was not forbidden at any stage. This is why the Mehaber permits eating this fish with dairy. With a prohibition (איסור), however, even several נ"ט בר נ"ט remain forbidden (Taz sk1). The Rama is stringent lechatchila for roasting and cooking, but permits bedieved, permits the use of their own dishes, and permits when the food was only 'risen' (עלו) without cooking or when the dish is not ben yomo. For practical halacha, consult your Rav.

This is the central case of dishwashing (se'if 3). According to the Mehaber, meat plates washed in a dairy cauldron (יורה) with boiling water (yad soledet), even both ben yomo, are permitted on the grounds of נ"ט בר נ"ט דהיתרא, provided one can say 'I am certain no fat was stuck to it' (ברי לי). The Rama forbids when both are ben yomo, washed together and in a כלי ראשון — and such is the custom; but he permits if one is not ben yomo, or if they were washed one after another, or in a כלי שני. עירוי (pouring) from a meat כלי ראשון counts as a כלי ראשון, but neutral boiling water poured over both is permitted. For practical halacha, consult your Rav.