The Ran explains (1a in the Rif’s pages) according to Rashi's approach: "One can say that according to Torah law, either of the two suffices, meaning either checking for chametz or nullifying it, because checking alone also works, as we say in the Gemara (7b) 'from where do we know that we check by candlelight?' and we derive it from verses. This implies that checking is also from the Torah, and anyone who has checked does not need to nullify from the Torah's perspective. Therefore, it is reasonable to say that checking is to avoid the prohibition of possessing chametz, and that the Sages required nullification after checking only as a precaution lest one finds a nice piece of chametz and becomes fixated on it, as stated in the Gemara (6b)."

The Ran proves that there is a Torah source for both checking and nullification: "You might say, if so, we have from the Torah only this nullification, and checking and destroying chametz are not required by the Torah at all. It is impossible to say this, as the Gemara (7b) inquires, 'from where do we know that we check by candlelight?' and we derive it from verses. And if you say it is merely a rabbinic hint, that is not so, for we see that the Tannaim disputed (21a) about how chametz is to be destroyed, with some saying that the only valid destruction of chametz is burning, and Rabbi Yehuda who holds this view (27b) derives it from leftover sacrifices (notar). And if you say that the Torah only mandates nullification, what is this destruction that they disputed about? It is clearly proven in the Gemara that they argued about Torah law, as Rabbi Akiva (5a) says, 'we find that burning is a primary labor, and the Torah said to remove leaven from your houses.'"