I'm not sure what standard you're using for "proven," but there are a lot of studies showing results similar to this one:
https://www.publichealth.columbia.edu/news/calorie-restricti...There don't seem to be any huge, long-term studies, but here is a review of what's available as of a few years ago: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7468870/