Reference for Eruvin 81:12
הכי נמי מסתברא
was] that [the day had been their] festival, but on the eve of [their] festival<span class="x" onmousemove="('comment',' Sc. the usual date of the Ninth of Ab which is the proper fast day and which always occurred on the eve of their festival.');"><sup>33</sup></span> they did complete the fast, did they not?<span class="x" onmousemove="('comment',' Which proves, since R. Eleazar son of R. Zadok was a contemporary of R. Gamaliel (cf. Bezah 22a) , that on the eve of a festival a fast was completed even in the days of R. Gamaliel,');"><sup>34</sup></span> Rabina replied: A festival of Rabbinic origin<span class="x" onmousemove="('comment',' Lit., 'their words'.');"><sup>35</sup></span> is different [from a Sabbath]. Since it is permitted to fast for a number of hours on the former<span class="x" onmousemove="('comment',' As was stated supra, 'When we fasted etc.'');"><sup>36</sup></span> it is also permitted to complete a fast on its eves;<span class="x" onmousemove="('comment',' The completion of the fast does not involve even a full hour. If one may fast on a Rabbinic festival one should certainly be allowed on it a fast lasting only a portion of an hour.');"><sup>37</sup></span> [but as regards] the Sabbath, since it is forbidden to fast on it even for a few hours, it is forbidden to complete a fast on its eves.<span class="x" onmousemove="('comment',' Where the fast is to be completed its termination would encroach upon the Sabbath and one would incur the guilt of fasting on a Sabbath, however short the duration of that fasting might be.');"><sup>38</sup></span> 'I have never heard', said R'Joseph, 'that tradition',<span class="x" onmousemove="('comment',' Ulla's (supra) that the halachah is in agreement with R. Jose.');"><sup>39</sup></span> Said Abaye to him, 'You yourself have told it to us<span class="x" onmousemove="('comment',' R. Joseph lost his memory as a result of a serious illness and his students often reminded him of traditions and rulings he had imparted to them in his earlier days.');"><sup>40</sup></span> and you said it in connection with the following: "No fast may be imposed upon the public on New Moons etc. " and it was in connection with this that you told us, "Rab Judah said in the name of Rab: This is the view of R'Meir<span class="x" onmousemove="('comment',' Who stated supra that the fast is not to be completed, and the same applies to the fast of the Ninth of Ab that fell on a Sabbath eve.');"><sup>41</sup></span> who laid it down in the name of R'Gamaliel; but the Sages ruled: One must complete the fast". Now does not this<span class="x" onmousemove="('comment',' The ruling of the Sages.');"><sup>42</sup></span> refer to all the days mentioned?<span class="x" onmousemove="('comment',' Lit., 'on all of them', i.e., that even on a Sabbath eve the fast must be completed. Now since Rab described R. Jose by the plural noun of 'Sages' it is obvious that he intended the halachah to be in agreement with his view.');"><sup>43</sup></span> - No; only to Hanukkah and Purim. This may also be supported by a process of reasoning