Gemara

'Mitzvah' refers to Arayos mid'Rabanan. They are called (Isurim of) Mitzvah, for it is a Mitzvah to obey Chachamim (who decreed about them):

Kidushin 50a (Mishnah): Likewise, for Gitin of divorce and freedom, we force the husband or master until he says 'I want to give it'.

Inference: It is valid even though he was forced, and he does not really want! This shows that thoughts in the heart are ignored!

Rejection: There is different, for it is a Mitzvah to obey Chachamim.

Shabbos 23a - Question: We bless '...Asher Kidshanu b'Mitzvosav v'Tzivanu Lehadlik Ner Shel Chanukah'. Where did Hash-m command this?

Answer #1 (Rav Avya): "Lo Sasur" (do not deviate from what Chachamim say).

Answer #2 (Rav Nechemyah): "She'al Avicha v'Yagedcha Zekenecha va'Yomru Lach".

Question (Rav Amram): If we bless on all Mitzvos mid'Rabanan, we should bless on tithing Demai (Peros of an Am ha'Aretz. They are Safek Tevel)! 1. Answer #1 (Abaye): We bless on all Vadai Mitzvos mid'Rabanan, but not on tithing Demai, for it is a Safek (perhaps it was already tithed).

Answer #2 (Rava): (We bless even on Safek Mitzvos mid'Rabanan.) It is a mere stringency (not a Safek) to tithe Demai, for most Amei ha'Aretz tithe.

Chulin 106a (Rav Idi bar Avin): We wash before a meal of Chulin in order that we will be accustomed to guarding our hands from Tum'ah, so we will not impart Tum'ah to Terumah. Also, it is a Mitzvah.

(Abaye): It is the Mitzvah to obey Chachamim.

Rishonim

Rambam (Hilchos Eruvin 6:24): Just like we bless on Eruvei Chatzeros and Shitufei Mavo'os (which allow carrying in a Chatzer or alley), we bless on Eruvei Techumin (to permit going more than 2000 Amos from the city).

Rebuttal (Ra'avad): How can one bless 'and He commanded us' for Eruvei Techumin? This is a leniency. We are not commanded to do so!

Migdal Oz (DH va'Ani): We are commanded Lo Sasur. It is a Mitzvah to heed Divrei Chachamim, to be lenient or stringent.

Rambam (Hilchos Berachos 11:3): We bless 'and He commanded us' even for Mitzvos mid'Rabanan. Hash-m commanded us to heed (Chachamim), and among their Mitzvos are to light Ner Chanukah, Kri'as ha'Megilah...

Ohr Some'ach (Hilchos Milah 3:6): The Rambam holds that we do not bless on any Safek. Chachamim did not command about this at all. The Torah forbids (Stam), and we must be stringent.

Note: The Rambam (Hilchos Kilayim 10:27) holds that it is only mi'Divrei Sofrim that we are stringent about a Safek Torah! Often, when Chachamim expounded a law, the Rambam calls it mi'Divrei Sofrim, but there he says that since it is only mi'Divrei Sofrim, they were lenient when they wanted!

Shevet ha'Levi (10:110): We bless 'and He commanded us' for Ner Chanukah. Does this mean that Hash-m commanded us to heed Chachamim, due to "Lo Sasur" or "She'al Avicha...", and they commanded about Ner Chanukah? Or, perhaps Hash-m commanded, but the command came through Chachamim? The Rambam explains the first way. However, this is because he holds (Hilchos Mamrim 2:9) that if one makes a mid'Rabanan law totally mid'Oraisa, he transgressed Bal Tosif. The Gemara asked that we bless on Ner Chanukah like on Mitzvos mid'Oraisa, so there is concern for Bal Tosif! (One opinion in the Yerushalmi holds that we bless 'on the Mitzvah of (heeding) Chachamim' due to this concern!) Therefore, he explains that we bless on the Mitzvah to heed Divrei Chachamim, to show that it is not mid'Oraisa. However, the Ra'avad holds that Bal Tosif does not apply to mid'Rabanan enactments. The Gemara asked simply what is the source to bless on Ner Chanukah, and answered that due to Lo Sasur or She'al Avicha, it is as if Hash-m commanded about it.

Rambam (Hilchos Mamrim 1:2): Anyone who does not do like the ruling of the Great Sanhedrin transgresses the Lav "Lo Sasur". One is not lashed for this, for one can be killed for it, i.e. a Zaken Mamrei (who rules unlike them). This applies to traditions, i.e. oral Torah, things expounded through the Midos, and fences made for the Torah according to the needs of the time, i.e. decrees, enactments and customs. It is an Aseh to obey all these, and a Lav to transgress.

Lechem Mishneh: The Ramban (Sefer ha'Mitzvos, Shoresh 1) asked, if so, there is a Lav and Aseh to fulfill all mid'Rabanan laws. We should be more stringent about mid'Rabanan laws than mid'Oraisa laws! Kiryat Sefer answered that Chachamim stipulated that one who transgresses their words is not like one who transgresses Torah, and that one may be lenient about a Safek. The Rambam says that (even so) there is a Lav and Aseh, i.e. for a Zaken Mamrei. The Lav and Aseh do not apply to one who transgresses a mid'Rabanan law, even b'Mezid, if he does not deny the law.

Acharonim

Chasam Sofer (EH 116): A man married a woman without telling her that he is epileptic. She does not want to live with him, and he refuses to divorce her. The Mordechai citing Avi ha'Ezri holds that we do not force him to divorce her, and the Rosh holds that we force him. Even if Hash-m knows that the Halachah follows the Rosh, since the Mordechai argues and we cannot decide, if one was forced to divorce, mid'Oraisa she is married. It is not a Safek. A forced Get is valid because we assume that a man wants to fulfill Divrei Chachamim. This is when the husband knows that they properly force him. Here, he can say 'who says that I must heed the Rosh? Perhaps I should heed the Mordechai!' Therefore, we cannot force him.

Chedvas Yakov (YD 24): It seems that Shiduchin is a Mitzvah, for Rav lashes for Kidushin without Shiduchin (Kidushin 12b). It is a Mitzvah to obey Chachamim.

Igros Moshe (CM 2:24): Chachamim are pleased with one who pays a debt after Shemitah (even if the lender did not write a Pruzbul. This implies that it is improper not to pay. Rabah was upset with one who offered to pay, and (after Rabah said that he is Meshamet, i.e. does not demand payment) he did not say 'I want to pay anyway' (Gitin 37b). The lender may hang him until he says this. Surely, it is not merely praiseworthy! If one is coerced to give a gift, it is invalid! Rather, Chachamim obligate doing so, and Mitzvah to heed Divrei Chachamim.

Note: The Gemara said so only when the borrower offered to return it. Surely, we cannot learn to a case when he says that he cannot pay.

Va'Ya'an Yosef (OC 43): Since the Ari Zal commanded to immerse in a Mikveh on Shabbos morning, it is a Mitzvah to heed Chachamim, therefore, one may make an Eruv Techumin for this, even though it is permitted only for Mitzvos.

Va'Ya'an Yosef (OC 317): According to Tosfos, why is burning Chametz (found on Pesach, after he did Bitul) forbidden only mid'Rabanan? The Torah permits only what is needed for the day! We can say that since Chachamim said to burn it, doing so is not Meleches Avodah, rather, the Mitzvah to heed Divrei Chachamim.

Tzitz Eliezer (1:27:6): The Shitah Mekubetzes (Kesuvos 3a DH Od) says that (if one sent a Get and was Mevatel it,) Chachamim uprooted the Kidushin from the beginning, and made the Bi'ah Bi'as Zenus. The husband did not want Bi'as Zenus. However, they can make it Bi'as Zenus, even though he did nothing wrong, for he was Mekadesh based on Chachamim's will, and it is a Mitzvah to heed Divrei Chachamim.

Yabi'a Omer (4 EH 15:2): If the Yevamah does not want to do Yibum, we tell the Yavam to do Chalitzah. Since it is a Mitzvah to heed Divrei Chachamim, "nothing bad will occur to a Tzadik." Rather, he will be rewarded. In any case, many say that Chalitzah is always preferable.

Yachel Yisrael (8): Sefer ha'Zichronos (1:1) asks, how could the Rambam say that the Mitzvah to heed Divrei Chachamim does not apply today? Surely it is not only to heed the Great Sanhedrin. Rather, it is a printing mistake. It should say regarding the Mitzvah to heed a Navi that it does not apply today. Also Sefer ha'Chinuch says that the Mitzvah to heed Chachamim, their decrees and Halachos applies even nowadays.

Da'as Kohen (YD 55 DH v'Al): Since Chachamim forbade fish with meat due to danger, it is like an Isur, and one may not be Mevatel it l'Chatchilah, i.e. to add until there is a Shi'ur for Bitul. However, we do not say so about all dangers. Some poisons, in a very small dosage, are curative, and are good to eat when diluted. It is unreasonable to forbid them. However, we can say that once Chachamim forbade them, the Mitzvah to obey Chachamim applies, and it is like Isur. Whatever Chachamim forbade, they forbade like Torah law, and it is forbidden even if the reason does not apply. Perhaps they had also other reasons.