The Talmud debates on which arm tefillin are worn, deriving from the word 'yadkha' (your hand) that it refers to the weaker arm (left for right-handed people), and also establishes from 'yad' — singular — that only one arm is intended.
רַבִּי נָתָן אוֹמֵר: אֵינוֹ צָרִיךְ, הֲרֵי הוּא אוֹמֵר: ״וּקְשַׁרְתָּם״ ״וּכְתַבְתָּם״ – מָה כְּתִיבָה בְּיָמִין, אַף קְשִׁירָה בְּיָמִין, וְכֵיוָן דִּקְשִׁירָה בְּיָמִין – הַנָּחָה בִּשְׂמֹאל הִיא. וְרַבִּי יוֹסֵי הַחוֹרָם, הַנָּחָה דְּבִשְׂמֹאל מְנָא לֵיהּ? נָפְקָא לֵיהּ מֵהֵיכָא דְּנָפְקָא לֵיהּ לְרַבִּי נָתָן. כְּתַנָּאֵי: ״יָדְכָה״ בְּהֵ״י – זוֹ שְׂמֹאל, אֲחֵרִים אוֹמְרִים: ״יָדְךָ״ לְרַבּוֹת אֶת הַגִּידֵּם. תַּנְיָא אִידַּךְ: אֵין לוֹ זְרוֹעַ – פָּטוּר מִן הַתְּפִילִּין, אֲחֵרִים אוֹמְרִים: ״יָדְכָה״ לְרַבּוֹת אֶת הַגִּידֵּם.
Rabbi Natan says: This proof is not necessary, as it says: “And you shall bind them for a sign upon your arm” (Deuteronomy 6:8), and then it states: “And you shall write them upon the doorposts of your house” (Deuteronomy 6:9). This teaches that just as writing is with the right hand, as most people write with their right hands, so too, the binding of phylacteries must be performed with the right hand. And since binding is with the right hand, this means that donning is on the left arm, as one cannot bind the phylacteries with the same hand upon which he is donning them. The Gemara asks: And from where does Rabbi Yosei HaḤorem, who holds that the right hand is also called yad in the Torah, derive that donning phylacteries is on the left arm? The Gemara answers: He derives it from where Rabbi Natan derives it. The Gemara notes that Rav Ashi’s opinion, that the halakha that phylacteries are donned on the left arm is derived from the term yadkha, is subject to a dispute between tanna’im, as it is taught in a baraita: Yadkha is written with a heh, indicating weakness, and this is referring to the left arm. Others say: “Your arm,” i.e., yadkha, serves to include one without a complete arm, i.e., one whose arm ends at the elbow, in the obligation to don phylacteries, as the remaining part is also categorized as a weak arm. It is taught in another baraita: If one does not have a left arm, i.e., not even above the elbow, he is exempt from the mitzva of phylacteries. Others say: Yadkha serves to include one without a left arm even above the elbow, teaching that he must don phylacteries on his right arm.