What you or I believe is not the issue - objectivism says that things are knowable without relying on anything but reason. So go ahead and reason your way into proving that good nutrition is better than bad nutrition, without simply substituting in your own preference for good nutrition, and without simply assuming it to be true and thereby taking it as true on faith. After all, if you can't prove it, how can you say that you "know" it to be true?
As I said, it's as 'proven' as "the sun is hot".
One bit of evidence that it *is* that proven is that you, yourself, believe it to be a proven fact.
In fact, I'd bet near to 100% of people you ask will agree it's a proven fact.
You're simply arguing to practice arguing.