Eruvin 41A

וכן ערב תשעה באב שחל להיות בשבת, אוכל ושותה כל צרכו, ומעלה על שולחנו אפילו כסעודת שלמה בשעתו. חל להיות תשעה באב בערב שבת ⁠— מביאין לו כביצה ואוכל, כדי שלא יכנס לשבת כשהוא מעונה.

and so too, on the eve of the 9th of Av that occurs on Shabbat, one need not reduce the amount of food he eats; rather, he may eat and drink as much as he requires and bring to his table a meal even like that of King Solomon in his time. If the 9th of Av occurs on Friday, we bring him an egg-bulk of food toward end of the day, and he eats it, so that he not enter Shabbat in a state of affliction.

תניא, אמר רבי יהודה: פעם אחת היינו יושבין לפני רבי עקיבא, ותשעה באב שחל להיות בערב שבת היה. והביאו לו ביצה מגולגלת, וגמעה בלא מלח. ולא שהיה תאב לה, אלא להראות לתלמידים הלכה.

It was taught in a baraita that R' Yehuda said: We were once sitting before R' Akiva, and it was the 9th of Av that occurs on Friday, and they brought him a slightly cooked egg, and he swallowed it without salt. And it was not that he desired it so much that he ate it; rather, he did so to show the students the halakha that one need not complete the fast when the 9th of Av occurs on Friday, so as not enter Shabbat in a state of affliction.

ורבי יוסי אומר: מתענה ומשלים. אמר להן רבי יוסי: אי אתם מודים לי בתשעה באב שחל להיות באחד בשבת, שמפסיק מבעוד יום? אמרו לו: אבל. אמר להם: מה לי ליכנס בה כשהוא מעונה, מה לי לצאת ממנה כשהוא מעונה.

And R' Yosei says: He must fast and complete the fast. R' Yosei said to the other rabbis: Don’t you agree with me with regard to the 9th of Av that occurs on Sunday, that one must stop eating on Shabbat while it is still day? They said to him: Indeed, we agree. R' Yosei said to them: What is the difference to me between entering Shabbat in a state of affliction and leaving it in a state of affliction? If one stops eating before Shabbat is over, he is spending part of Shabbat fasting, and yet even the rabbis concede that one must do so.