Your proposed axioms dont work. The problem is that they are not axiomatic at all. It is not at all self-evident that the god of the bible exists. This is a actually quite trivial to demonstrate: No culture that has exited in isolation from the bible has ever reproduced the biblical concept of god. Only cultures with access to the bible and other contemporary documents entertain the notion of a biblical god. If it were truly self-evident that the biblical god exists then we should not need a bible to know that, such being the nature of axioms. The next proposed axiom is problematic as well. First of all because it being true is contingent upon your first proposed axiom, which is false. Second, even if we grant, for the moment, that your first axiom is legitimate, the bible is so filled with inconsistencies, contradictions, inaccuracies, forgeries, that it could not possibly have been authored by any being claiming to be inerrant. In fact, cosmological information in the bible is exactly what you would expect for the time it was written, meaning there is no information in the bible that goes beyond a typical bronze age understanding of the world. If it were true that god authored the bible we should expect to see some evidence of a ground breaking scientific nature, but,even though we have had several such ground breaking scientific events, not one hint of them can be found, in retrospect or other wise, in the bible. What you have really done here confuse dogma with axiom.