So a witness changes their story on the stand and as a result your case is at risk of being directed out for insufficient evidence.  Can impeachment with a prior statement save the day?  Maybe… 

In order to present extrinsic proof of the prior statement, it will have to be authenticated by the impeached witness or a third party under Rule of Evidence 901.

The statement is defined as non-hearsay under Rule of Evidence 801(d)(1) if it is a prior inconsistent statement under oath.  It comes in for the truth of the matter asserted.  Under Rule of Evidence 613 a prior inconsistent statement technically is only admitted for purposes of challenging the person’s credibility. This because it still remains hearsay absent a non-hearsay use or a hearsay exception such as a statement of a party opponent under Rule of Evidence 801(d)(2) which is non-hearsay.

Under Rule of Evidence 801(d)(1) the prior inconsistent sworn statement provide substantive evidence of the contradicted fact. While the difference is technical, it can be of importance if the prior inconsistent statement is need to prove an essential element of your claim. 
Under Rule of Evidence 613 you need to do the following if you want to introduce extrinsic proof of the statement:
1. Authenticate the statement by identifying who, what, where and when the statement was made,
2. Give the witness an opportunity to explain or deny the statement, and 

3. Give the opposing attorney an opportunity to examine the witness about it. This includes allowing opposing counsel to review the impeaching statement if so requested.
Here’s the language from the rules…
Rule of Evidence  801(d)(1):
(d) Statements That Are Not Hearsay. Notwithstanding Rule 801(c) , a statement is not hearsay if:

(1) A Declarant-Witness’s Prior Statement. The declarant testifies and is subject to cross-examination about a prior statement, and the statement:

(A) is inconsistent with the declarant’s testimony and was given under penalty of perjury at a trial, hearing, or other proceeding or in a deposition;

Rule of Evidence 613:
Rule 613. Witness’s Prior Statement

(a) Showing or Disclosing the Statement During Examination. When examining a witness about the witness’s prior statement, a party need not show it or disclose its content to the witness. But the party must, on request, show it or disclose its contents to an adverse party’s attorney.

(b) Extrinsic Evidence of a Prior Inconsistent Statement. Extrinsic evidence of a witness’s prior inconsistent statement is admissible only if the witness is given an opportunity to explain or deny the statement and an adverse party is given an opportunity to examine the witness about it, or if justice so requires. This subdivision (b) does not apply to an opposing party’s statement under Rule 801(d)(2).

Hopefully, this discussion and these Rules show the importance of getting a sworn statement (preferably a deposition) from all key witnesses in advance of trial. A witnessed affirmation subject to the pains and penalties of perjury is adequate if notorization is not possible.