ki teitzei - How can the Rambam say that Kiddushin is a Mitzvah, against the Gemara?

The Rambam in Hilchos Ishus 1:1 makes the following statement:

כֵּיוָן שֶׁנִּתְּנָה תּוֹרָה נִצְטַוּוּ יִשְׂרָאֵל שֶׁאִם יִרְצֶה הָאִישׁ לִשָּׂא אִשָּׁה יִקְנֶה אוֹתָהּ תְּחִלָּה בִּפְנֵי עֵדִים וְאַחַר כָּךְ תִּהְיֶה לוֹ לְאִשָּׁה שֶׁנֶּאֱמַר (דברים כב יג) "כִּי יִקַּח אִישׁ אִשָּׁה וּבָא אֵלֶיהָ":

Once the Torah was given, the Jews were commanded that if a man wants to marry a woman, he should take her first before witnesses, and afterwards she should be to him as a wife, as it says, “When a man takes a woman and comes upon her” (Devarim 22:13).

The Rambam clearly states that Kiddushin is a mitzvah (he should take her before marrying her - in the Hebrew text, the marriage is referred to as לשא, a form of נשואין, Nisuin, the second stage of marriage; therefore, this must refer to the first stage of marriage, Kiddushin).

Now read the Gemara in Moed Kattan 18b. Shmuel said that Kiddushin is permissible on Chol HaMoed, and the Gemara proposed that the fact that the earlier mishnah (Moed Kattan 8b) only forbade Nisuin, it must be that Kiddushin is permissible. The Gemara refutes this proof:

לא מיבעיא לארס דלא קעביד מצוה אלא אפילו לישא נמי דקא עביד מצוה אסור

[The Mishnah means to say:] It goes without saying that Eirusin [i.e. Kiddushin], by which he is not doing a Mitzvah, [should be forbidden,] but even Nisuin also, by which he does a Mitzvah, is forbidden.

Um...

How can the Rambam learn that Kiddushin is a Mitzvah, when the Gemara explicitly states that Kiddushin is not a Mitzvah?!

Answer

Rambam's son, R. Avraham, as cited in Kesef Mishne, end of Ishus 1:1, answers that the command is to marry with kidushin and nisuin, which is why Rambam refers to even the first part as a mitzva, meaning the start of one, but doing the first part alone doesn't do a mitzva. KM implies by his wording, q.v., that the main part of the dual mitzva is the second part.

h/t R. Tz'vi Hirsh Chiyes