Is evidence impeaching a witness's credibility relevant?

Evidence impeaching a witness's credibility is relevant. Evidence Code section 780 defines what a jury may consider to appraise the credibility of a witness: "[T]he court or jury may consider . . . any matter that has any tendency in reason to prove or disprove the truthfulness of [a witness's] testimony at the hearing, including but not limited to any of the following: [] . . . [] (f) The existence or nonexistence of a bias, interest, or other motive." "As with all relevant evidence, however, the trial court retains discretion to admit or exclude evidence offered for impeachment. [Citations.] A trial court's exercise of discretion in admitting or excluding evidence is reviewable for abuse [citation] and will not be disturbed except on a showing the trial court exercised its discretion in an arbitrary, capricious, or patently absurd manner that resulted in a manifest miscarriage of justice [citation]." (People v. Rodriguez (1999) 20 Cal.4th 1, 9-10.)