Niddah, Chapter 6, Mishnah 5. This portion of the chapter is devoted to paired rulings that all follow a single form: whoever is fit for one thing is automatically fit for a second, while someone fit for the second is not necessarily fit for the first. Our mishnah applies that form to the courtroom, first to judges and then to witnesses.
The mishnah's opening clause reads "Kol haroui ladun dinei nefashos": whoever holds the standing to sit on a court trying dinei nefashos, capital cases, where a defendant's very life rests on the verdict, is by that very fact "roui ladun dinei mamonos", competent to rule in dinei mamonos as well, disputes over money and property.
And then the other direction: "V'yeish sheroui ladun dinei mamonos v'eino roui ladun dinei nefashos." There are people who are indeed qualified to judge monetary cases, and yet those very people are not qualified to judge capital cases. Fitness for dinei nefashos always includes fitness for dinei mamonos, but fitness for dinei mamonos does not always include fitness for dinei nefashos.
The Mishnah continues with a second pair, this time linking the role of the judge to the role of the witness: "Kol hakasher ladun, kasher l'hoid." Anyone who is fit to serve as a judge is also fit to serve as a witness in court.
Here too the Mishnah completes the pattern: "V'yeish shekasher l'hoid v'eino kasher ladun." There are people who are perfectly fit to give testimony, and nevertheless those same people are not fit to serve as judges.
So the mishnah gives us two one directional rules. Qualification for the more demanding role, judging capital cases in the first case and judging altogether in the second, carries the lesser qualification with it, while qualification for the lesser role stands on its own and does not reach upward.