While for many religion forms the basis of many of their core axiomatic values, I don't agree that the converse holds true as well. If A then B does not necessarily imply that if B then A.

Personally, I feel that religion is more along the lines of core axiomatic spiritual beliefs, in particular regarding the self as it relates to both society, the universe, and any dieties one believes in. Your definition far exceeds that scope, and would encompass the foundations of science, which I argue can coexist harmoniously with religion (though it so often doesn't) but should not be confused with it.

Of course, my definition is tossed out there with far less than consideration than such a weighty question deserves.