The limitation of a kal vekhomer TB Yevamot 22

Daf TB Yevamot 22 analyzes the disagreement between the Rabbis and Rabbi Yosi ben Yehudah concerning the case when a man unwittingly was intimate with his sister who was also the daughter of his father’s wife. The rabbis maintain that this man must bring two khatats (חטאת) sin, sacrifices because he transgressed two prohibited liaisons, his sister and the daughter of his father’s wife. Based upon his interpretation of Leviticus 18:11, Rabbi Yosi ben Yehudah holds that the man needs only to bring one khatat. The Gemarra goes back and forth why and how each side understands their opponent's verses differently. What interested me was a general rule concerning the kal vekhomer (קַּל וָחֹֽמֶר), A conclusion drawn from a minor or lenient law, to a major or more strict one.

The daf sets the stage for this conclusion.

“And Rabbi Yosei, son of Rabbi Yehuda, says: The verse states: “She is your sister,” which comes to limit and emphasize that you hold him liable due to the fact that she is his sister but you do not hold him liable a second time due to the fact that she is also his father’s wife’s daughter.

“And what do the Rabbis do with this verse: “She is your sister”? They require it in order to hold him liable to receive punishment for having relations with his sister who is both the daughter of his father and the daughter of his mother, to say that the Sages do not derive an additional Torah prohibition by way of a logical derivation, i.e., an a fortiori inference. In other words, although it would seem that since he is liable to receive punishment for having relations with his father’s daughter and also for his mother’s daughter, this must be all the more true in a case where she is the daughter of both his father and his mother, yet nevertheless, there is no new prohibition here. Therefore, the matter was taught explicitly in the Torah, to teach that the Sages may not derive additional prohibitions by way of a fortiori inferences. (kal vekhomer)” (Sefaria.org translation)

A kal vekhomer can’t produce a brand new Torah prohibition. It can only create a permission or a prohibition within a specific existing halakha.