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In Hilkhoth Tefillin 4:10, the Rambam states the basic and well-known halakhah that "...shabbathoth wi-yamim tovim enan zeman tefillin..." (Translation: "Shabbat and Yom Tov are not times for [wearing] tefillin"). This is due to the pasuq that tefillin are meant to be an oth ("sign") [cf. Shemoth 13:9; Devarim 6:8, 11:18, et al] and Shabbath and Yamim Tovim are already an oth by themselves [cf. Shemoth 31:17; Hilkhoth Tefillin ibid.]

However, there is an interesting statement in Hilkhoth Evel 10:10 which says:

הקובר את מתו ביום טוב שני שהוא יום טוב האחרון או ביום טוב שני של עצרת נוהג בו אבילות: הואיל ויום טוב שני מדבריהם ואבילות יום ראשון מן התורה יידחה עשה של דבריהם מפני עשה של תורה. אבל אם קבר ביום טוב שני של ראש השנה אינו נוהג בו אבילות ששניהן כיום אחד ארוך הן מהטעם שביארנו בהלכות קידוש החודש

Translation: "The one who buries his dead on the second day of Yom Tov [yom tov sheni], which is the last Yom Tov, or on the second day of the Yom Tov of Shemini Assereth, conducts himself on it according to all the rules of mourning. Since the second day of Yom Tov [yom tov sheni] is rabbinic in nature and the first day of mourning in Biblical in nature, the positive commandment of the rabbis is displaced by the positive commandment of the Torah. But if one buried [his dead] on the second day of Yom Tov [yom tov sheni] of Rosh HaShannah, he does not conduct himself on it [according to all the rules of] mourning since both days are together considered one long day for the reason that we explained in Hilkhoth Qidhush HaHodhesh."

In this halakhah, the Rambam seems to communicate a general principle that any misswath `aseh (positive commandment) from the Torah displaces a positive directive of rabbinic enactment - in this case, Yom Tov Sheni.

So, my question is, if the gezerah of Yom Tov Sheni does not displace aveyluth [halakhic mourning] since it is a misswath `aseh min ha-torah, then why would it displace the obligation to wear tefillin, since it is also a positive commandment on a Biblical level?

(NOTE: I am assuming the position that tefillin must be worn on Holo Shel Mo`edh and that the Rambam also takes this position in the Mishneh Torah.)

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The Rambam himself says in הלכות שביתת יום טוב - פרק ראשון

כב יוֹם טוֹב שֵׁנִי אַף עַל פִּי שֶׁהוּא מִדִּבְרֵי סוֹפְרִים כָּל דָּבָר שֶׁאָסוּר בָּרִאשׁוֹן אָסוּר בַּשֵּׁנִי. וְכָל הַמְחַלֵּל יוֹם טוֹב שֵׁנִי וַאֲפִלּוּ שֶׁל רֹאשׁ הַשָּׁנָה בֵּין בְּדָבָר שֶׁהוּא מִשּׁוּם שְׁבוּת בֵּין בִּמְלָאכָה בֵּין שֶׁיָּצָא חוּץ לַתְּחוּם מַכִּין אוֹתוֹ מַכַּת מַרְדּוּת אוֹ מְנַדִּין אוֹתוֹ אִם לֹא יִהְיֶה מִן הַתַּלְמִידִים. וּכְשֵׁם שֶׁהָרִאשׁוֹן אָסוּר בַּהֶסְפֵּד וְתַעֲנִית וְחַיָּב בְּשִׂמְחָה כָּךְ הַשֵּׁנִי וְאֵין בֵּינֵיהֶן הֶפְרֵשׁ אֶלָּא לְעִנְיַן מֵת בִּלְבַד:‏

See the מגיד משנה there who brings sources, explaining that essentially both days of Yom Tov have the identical status, with the exception of certain Halachot related to burying and mourning.

In other words, the question is the other way round: Why is some form of mourning allowed, since the 2 days of Yom Tov are identical?

The answer - based in the sources (ibid) - seems to be that we pasken like Rav Ashi in ביצה Daf 6a:

רב אשי אמר אפילו לא אישתהי מ''ט יו''ט שני לגבי מת כחול שויוה רבנן

Even if there's no risk of the body decaying, the 2nd day of Yom Tov has the status of a weekday as regards burial.

As I understand it, when they decreed the 2nd day of Yom Tov, they excluded burial and essential mourning - and hence it (and only it) is allowed. The Rambam reinforces this by reminding you it's a Torah obligation to mourn on the first day, and you may not choose to forgo your mourning in honour of Yom Tov.

With regards to Tefillin, they did included it in the decree - and therefore one may not wear Tefillin on 2nd day Yom Tov.

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