Procedure for deductive theorem proof done in axiomatic logic

In the wikipedia article Deduction theorem - Wikipedia, the free encyclopedia under the section titled "Conversion from proof using the deduction meta-theorem to axiomatic proof", it explains there is a procedure for converting a Deduction Theorem proof to a proof in axiomatic logic. I tried to follow the description but was unable to generate the axiomatic proof. I am looking for someone who can help me understand this procedure.

Given some conditional A -> B, which can be proven by A |- B => |- A -> B (via Deduction Theorem), what is the procedure/process for generating an equivalent proof of A -> B in only axiomatic logic (without the Deduction Theorem).

Thanks.