Is impeachment evidence establishing a motivation to lie relevant?

Here, the court ruled the evidence was irrelevant, and did not make a ruling on the prosecutor's Evidence Code section 352 objection. It is true impeachment evidence establishing a motivation to lie can be relevant because evidence is "relevant" if it has any tendency in reason to prove or disprove any disputed fact of consequence, including evidence relevant to the credibility of a witness. (Evid. Code, 210, 780, subd. (f).) Further, "[a]s a general matter, a defendant is entitled to explore whether a witness has been offered any inducements or expects any benefits for his or her testimony, as such evidence is suggestive of bias. [Citations.]" (People v. Brown (2003) 31 Cal.4th 518, 544.) But that is not the end of the inquiry.