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Full Idea
For Frege, no arithmetical statement is an axiom, because all are provable.
Gist of Idea
Arithmetical statements can't be axioms, because they are provable
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Tyler Burge - Frege on Knowing the Foundations 1
Book Ref
Burge,Tyler: 'Truth, Thought, Reason (on Frege)' [OUP 2001], p.325
A Reaction
This is Frege's logicism, in which the true and unprovable axioms are all found in the logic, not in the arithmetic. Compare that view with the Dedekind/Peano axioms.