A better example is the well-ordering of the reals. From wikipedia:
From the [axioms of math] one can show that there is a well-order of the reals; it is also possible to show that [those axioms] alone are not sufficient to prove the existence of a definable (by a formula) well-order of the reals.
Absolutely nothing like the proposition that god exists, and I wag my finger at you for associating the concrete facts of mathematics with superstitious claims backed up by hearsay.
From the [axioms of math] one can show that there is a well-order of the reals; it is also possible to show that [those axioms] alone are not sufficient to prove the existence of a definable (by a formula) well-order of the reals.
http://en.wikipedia.org/wiki/Well-order
So you can prove that set of real numbers can be well-ordered, but you can also prove that an order cannot be defined.
Kind of how God exists, but cannot be perceived or comprehended ;)
(or maybe not)