Note that the proof does not say that professed unbelievers do not prove things. The argument is that you must borrow from the Christian worldview, and a God who makes universal, immaterial, unchanging laws possible in order to prove anything.
In logic, this type of proof is called 'transcendental logic,' or 'the impossibility of the contrary,' where God is the basis for any rational thought. Only the Christian worldview can logically support rationality.

