Commento su Tohorot 2:3

הראשון שבחולין טמא ומטמא – [defiles] heave-offering/priest’s due, that a loaf of heave-offering that came in contact with first-degree [of ritual impurity] of unconsecrated foods, becomes second-degree [of ritual impurity] and makes third-degree [of ritual impurity] unfit/invalid.

Introduction Our mishnah provides some basic rules as to the implications of the levels of impurity in common food, meaning non-sacred food, neither terumah nor sacrifices.

והשני שבחולין – makes heave-offering unfit/invalid but does not defile, for third-degree [of ritual defilement] of heave-offering does not make something fourth-degree [of ritual defilement], therefore third-degree [of ritual defilement] of heave-offering is not considered defiled, but rather unfit/invalid.

First [degree uncleanness] in common food is unclean and conveys uncleanness; Hullin (regular or common food) that has first degree uncleanness can defile other foods, giving them second degree uncleanness.

והשלישי של חולין – this is what he said and if there is in those unconsecrated foods third-degree [of ritual impurity] as, for example, that they became through the purification of heave-offering/priest’s due.

Second [degree uncleanness] invalidates but does not convey uncleanness. Hullin that has second degree uncleanness invalidates other food. If the other food is terumah, the terumah is invalid. If the other food is hullin which the person wishes to eat with the sanctity of terumah, then it is invalid. But it doesn't give other food third degree impurity.

נאכל בנזיד הדמע (is consumed in a pottage of Holy Things)- in a cooked dish [that heave-offering] is mixed in, for the heave-offering/Terumah is called דמע/Holy Things (i.e., another name for Terumah) , as it is stated (Exodus 22:28): "מלאתך ודמעך לא תאחר [בכור בניך תתן-לי]"/You shall not put off the skimming of the first yield of your vats. [You shall give to Me the first-born among your sons],” and in the second chapter of [Tractate] Hullin (folio 34b), it proves that specifically, when there isn’t in the pottage of Holy Things an olive’s bulk of heave offering incidentally for consuming a certain quantity of bread (i.e., a piece, which is defined by the Tosefta Negaim, Chapter 7, Halakha 10 as half a loaf of which three make a Kab) that permits him to eat food which is third-degree [of ritual impurity], but if there is an olive’s bulk of heave-offering incidentally for consuming a certain quantity of bread (i.e., half a loaf), it is prohibited, for we hold that a person who consumes that which is third-degree [of ritual impurity] from unconsecrated food, that was made through the purification of Terumah/heave-offering, his body is made unfit from consuming heave-offering.

And third [degree uncleanness] may be eaten in a dish mixed with terumah. Basically, there is no such thing as hullin with third degree impurity. If food came into contact with other hullin food with second degree impurity, that food can be eaten in a dish with terumah because it is not all impure.