I've heard that there is no concept of ביטול regarding חמץ. If that is true then is a Davar ha'mamid an issur d'oraisa on pesach?
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That which chometz is not בטל in any amount is a d'rabanan (Mishnah Berura 447:1). Its lack of bittul cannot therefore create an issur d'oraisa.
The question depends on whether the item is before or during Pesach. During Pesach chametz is asur bemashehu and cannot be made batel. Before Pesach, it is permitted and can be made batel (with various specific limitations). For example, one can purchase milk before Pesach without certification, but in must be certified as Koser for Pesach when purchased on Pesach.
Here is what the OU says.
I double checked with my Rav and he confirmed that bitul only takes place if it is owned by a Jew. Thus, a Jewish owned store can continue to sell milk that came in before Pesach. However, a Jew cannot purchase milk from a nonJewish store on Chol Hamoed even though the milk arrived in the store before Pesach. Since he is purchasing it on Pesach and the bitul did not take place, it is asur bemashehu.