Phase I/II trials do not "prove" anything, and for that matter no study does. The Phase II data were persuasive enough to warrant start of a Phase III with a larger patient population, but there is zero reason to expect that Phase III will give identical results to Phase II. If it were other, than FDA would simply take Phase II data and approve the drug, but they don't do that for some very good reasons. The history of pharma and biotech is littered with the bodies of companies that failed to repeat the results of Phase II in the pivotal Phase III trial.
If you want to be rigorous, take the Phase II results and the number of patients treated and calculate the resulting confidence interval. It will be wider than you think.