Eruvin 39B

ורבנן, התם כי היכי דלא לזלזולי ביה.

And the Rabbis hold that there, the 1st day is not observed as a Festival by Torah law but due to rabbinic decree, so that people will not demean the day in future years and end up desecrating the Festival should the witnesses come on time. However, by Torah law it is an ordinary weekday, and therefore one can establish two separate eiruvin for the two days.

ועוד אמר רבי יהודה וכו׳.

We learned in the Mishnah that in addition to his ruling with regard to eiruvin for the two days of Rosh HaShana, R' Yehuda said further that the two days can be split with regard to a basket of tevel produce and an egg laid on the 1st day of the Festival.

וצריכא. דאי אשמעינן ראש השנה ⁠— בהא קאמר רבי יהודה, משום דלא קעביד מידי. אבל כלכלה, דמיחזי כמתקן טיבלא ⁠— אימא מודה להו לרבנן.

The Talmud comments: And it was necessary to teach us all 3 laws, as they could not have been derived from one another. As, if he had only taught us the halakha with regard to establishing an eiruv for the two days of Rosh HaShana, one might have said that only in this case does R' Yehuda say his ruling because in this case one does not actually do anything on the Festival itself. But in the case of a basket, where it appears as though one is rendering tevel fit on a Festival, say that R' Yehuda concedes to the Rabbis that it is decreed prohibited.

ואי אשמעינן הני תרתי ⁠— משום דליכא למיגזר עלייהו. אבל ביצה, דאיכא למיגזר בה משום פירות הנושרין ומשום משקין שזבו ⁠— אימא מודה להו לרבנן, צריכא.

And had he taught us only these two halakhot, we might have said that R' Yehuda is lenient because there is no reason to issue a decree prohibiting them, as the potential prohibitions involved are not so severe. But in the case of an egg that was laid on the 1st day of a Festival, where there is reason to issue a decree prohibiting it, as explained in tractate Beitza, because of fruit that fall from a tree or due to liquids that oozed from fruit on a Festival, both of which the rabbis prohibited as a safeguard against violating Torah prohibitions, say that R' Yehuda concedes to the opinion of the Rabbis, which maintains that this egg may not be eaten even on the 2nd day of the Festival. It was therefore necessary to teach us all 3 cases.