(Devarim 16:11) "And you shall rejoice before the L-rd your G-d": It is written here "rejoice," and elsewhere (Ibid. 27:7) "rejoice." Just as there, the rejoicing is with peace-offerings, here, too, it is with peace-offerings.
R. Yossi Haglili says: Three mitzvoth obtain on a festival: the festive offering (chagigah), the sacrifice of peace-offerings, viz. (27:7) "And you shall sacrifice peace-offerings and you shall eat them there"; "appearance" (re'iah), before the L-rd with a burnt-offering, viz. Shemoth 23:15); and rejoicing (simchah).
There obtains with re'iah what does not obtain with the others; with chagigah, what does not obtain with the others; and with simchah, what does not obtain with the others:
(דברים טז יא) וְשָׂמַחְתָּ, נֶאֶמְרָה כָּאן שִׂמְחָה וְנֶאֶמְרָה לְהַלָּן (דברים כז ז) שִׂמְחָה. מָה שִׂמְחָה הָאֲמוּרָה לְהַלָּן – שְׁלָמִים, אַף שִׂמְחָה הָאֲמוּרָה כָּאן – שְׁלָמִים.
(Devarim 16:11) "And you shall rejoice before the L-rd your G-d": It is written here "rejoice," and elsewhere (Ibid. 27:7) "rejoice." Just as there, the rejoicing is with peace-offerings, here, too, it is with peace-offerings.
אַתָּה וּבִנְךָ וּבִתֶּךָ וְעַבְדְּךָ וַאֲמָתֶךָ וְהַלֵּוִי אֲשֶׁר בִּשְׁעָרֶיךָ וְהַגֵּר, חָבִיב חָבִיב קוֹדֵם.
"you, your daughter, your man-servant, your maid-servant" — in order of affection.
רַבִּי יוֹסֵי הַגְּלִילִי אוֹמֵר: שָׁלֹשׁ מִצְווֹת נוֹהֲגוֹת בָּרֶגֶל, וְאֵלּוּ הֵן: חֲגִיגָה, רְאִיָּה, וְשִׂמְחָה.
R. Yossi Haglili says: Three mitzvoth obtain on a festival: the festive offering (chagigah), the sacrifice of peace-offerings, viz. (27:7) "And you shall sacrifice peace-offerings and you shall eat them there"; "appearance" (re'iah), before the L-rd with a burnt-offering, viz. Shemoth 23:15); and rejoicing (simchah).
יֵשׁ בָּרְאִיָּה שֶׁאֵין בִּשְׁתֵּיהֶן, בַּחֲגִיגָה שֶׁאֵין בִּשְׁתֵּיהֶן, בַּשִּׂמְחָה שֶׁאֵין בִּשְׁתֵּיהֶן.
There obtains with re'iah what does not obtain with the others; with chagigah, what does not obtain with the others; and with simchah, what does not obtain with the others:
רְאִיָּה – כֻּלָּהּ לַגָּבוֹהַּ, שֶׁאֵין בִּשְׁתֵּיהֶן.
re'iah (a burnt-offering) is entirely (consumed) for the Most High;
חֲגִיגָה – נוֹהֶגֶת לִפְנֵי הַדָּבָר וּלְאַחַר הַדָּבָר, שֶׁאֵין בִּשְׁתֵּיהֶן.
chagigah obtains both before the Word (the giving of the Torah) and afterwards;
שִׂמְחָה – נוֹהֶגֶת בָּאֲנָשִׁים וּבַנָּשִׁים, שֶׁאֵין בִּשְׁתֵּיהֶן.
simchah obtains with both men and women (as opposed to the others, which obtain only with men.)
הָא, מִפְּנֵי שֶׁיֵּשׁ בָּזוֹ מַה שֶׁאֵין בָּזוֹ, וְיֵשׁ בָּזוֹ מַה שֶׁאֵין בָּזוֹ – צָרַךְ הַכָּתוּב לוֹמַר אֶת כֻּלָּן.
This (i.e., their uniqueness) being so, Scripture had to mention all of them (individually, their not being mutually derivable.)