This is a case for the harder philosophies like philosophy of science and the paradox of Hempel's ravens. Hempel showed us that anything could prove any statement of logical equivalence. Most statements have a logical equivalent that encompasses a different set from itself and thus a differing set of objects etc. that count as corroboration. In Hempel's specific case, a white shoe is seen to be evidence for all raven's being black. With this in mind, yes proof exists, but is meaningless as everything is proof of everything else.