Burning chametz on the 15th (Pesachim 5a)

The gemara quotes R' Akiva's explanation that it must be that the mitzva of burning the chametz is on the 14th and not the 15th because the Torah couldn't possibly tell you to do it on the 15th when there is an av melacha of burning on Yom Tov. How does that prove anything? Maybe there is normally an av melacha of burning on yom tov but the Torah is telling you here that this is an exception and here you have a special mitzva to burn it on the 15th!

The Pnei Yehoshua answers that R' Akiva agreed with the limudim from earlier on the amud that "rishon" (either here or generally) could mean the day before. His only question was if it means the 14th only or the 14th and the 15th. He proves that it can't be the 15th also from the fact that you're not allowed to burn on yom tov. If it meant the 14th and 15th then it would mean that you'd have a choice and it would become a "davar she'efshar laasoso m'esmol" (something you could have done yesterday) so you would never be able to burn it on the 15th. Ergo, the Torah must have meant only the 14th.