Tis true, as Gnu Atheists, and non-Gnus who lean somewhat this direction point out, that in certain varieties of modern logic, one can prove the non-existence of something, ie, in this case the non-existence of god.
But wait, that's not all.
At the same time, one can also prove modern logic spinoffs of some classical arguments for the existence of god. Ask Alvin Plantinga about that. Well, actually, if one calls Satan perfectly evil, one can prove the existence of both, if you know from reading some discussions about that. So, yes, Gnus and others, you do get a "baby" with modern logic. You also get various sorts of "bathwater" that go along with it.
Hence, I still reject these arguments that say, "Hey, I can prove the non-existence of god." You can prove lots of things in modal logic and other modern logic systems which engage in multivariant thinking.
If you want your "baby," please be honest about accepting your "bathwater" at the same time.