The Tur (O”C 559) writes that one year Tisha B'av fell on Shabbos and it was pushed of to Sunday. Rabbeinu Ya'avetz was a Ba'al Bris and he davened Mincha early in the afternoon. He washed and did not complete his fast because it was a Yom Tov for him - and his source was the case of Rav Elazar bar Tzadok.
The Chasam Sofer (O”C 157) writes that the Yom Tov for the bringing of the wood was established before Tisha B’av and therefore takes precedence over Tisha B’av; however a bris milah where the obligation came about after the establishment of Tisha B’av does not take precedence and therefore they would be required to complete the fast.
The Chasam Sofer concludes that the proof is actually from Rabbi Elozar ben Rabbi Tzadok who was a kohen. He was a son-in-law of Sna’av as Tosfos in Eruvin (41) explains. It emerges that Tisha B’av should have taken precedence over his Yom Tov and nevertheless he did not conclude his fast. This was the proof of Rabbeinu Ya’avetz.