How have the courts treated the evidence in the case-in-chief in impeaching a defendant?

At the commencement of trial the prosecutor conceded the "confession" reportedly given by appellant to a police informant was inadmissible, as it was obtained in violation of appellant's Fifth and Sixth Amendment rights. The prosecutor did not seek to put the evidence on in the case-in-chief but sought to introduce the confession to impeach appellant, were he to testify. Ultimately, the trial court permitted the prosecutor to impeach appellant with the testimony of the police informant. Appellant urges reversal of his conviction on all counts claiming the contradictory prior statements made to the police informer should not have been admitted for impeachment purposes because they were obtained in violation of Miranda v. Arizona (1966) 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694.