And Maran the Gra"z (in the Haggadah, the piyyut Dayenu) explained differently, that all the plagues came in order to punish and bring judgments upon Egypt and their gods, while the plague of the firstborn came in order to facilitate the exodus of the Israelites from Egypt. He wrote that's why we mention only the plague of the firstborn in "emet ve-yatziv" because it is the reason for the exodus from Egypt, and the other plagues came to punish Egypt, not for the purpose of the exodus. Therefore, in the Hallel Hagadol, we only mention the plague of the firstborn, as it symbolizes the exodus from Egypt, as it is written immediately after: "And Israel went forth from among them." Therefore, the plague of the firstborn is mentioned alone in the piyyut "Dayenu" for this reason, as it symbolizes the good of the exodus from Egypt, not the punishments that the Egyptians received.

In any case, it is found, in both the interpretation of the Sforno and the interpretation of the Gra"z, that the plague of the firstborn was the reason for the exodus from Egypt, as the other plagues only came to bring them to repentance or to punish them in judgment, but not to force them to send the Israelites away. The plague of the firstborn came to compel them to send the Israelites, and therefore it is necessary to mention it in "emet ve-yatziv" together with the mention of the exodus from Egypt, as it is the reason for it.