I would have called these principles or laws rather than axioms. But what you call them makes no difference to the compelling body of evidence that justifies them.You want axioms of evolution?
1. Species come from other species
3. Species are naturally found near similar species
4. Species are found geographically close to fossils that most resemble them
5. Creatures found as fossils in rock are not identical to organisms alive today
6. Fossils deeper in rock strata (older), look less like animals alive today than those from shallower rocks(younger)
Stuart