Gemara

(Beraisa): All are obligated to wear Tefilin, even Kohanim.

"U'Kshartam l'Os Al Yadecha v'Hayu l'Totafos Bein Einecha" teaches that only one commanded to wear the Shel Yad is commanded to wear the Shel Rosh. Kohanim do not wear the Shel Yad during Avodah, for it would interrupt between Bigdei Kehunah and their skin. The Beraisa teaches that even so, they are commanded to wear Shel Rosh, for neither Tefilin is Me'akev the other.

Menachos 36a (Beraisa): One puts on the Shel Yad before the Shel Rosh, for it says "u'Kshartam l'Os Al Yadecha (and then) v'Hayu l'Totafos Bein Einecha." When removing them, he removes the Shel Rosh first.

(Rabah): We learn from "v'Hayu (plural) l'Totafos Bein Einecha" - whenever Tefilin are between your eyes, they must be two (you are wearing both).

37a - Question: What is R. Yosi's source that we wear Tefilin on the left hand?

Answer (Rav Ashi): (In one place) it says "Yadchah (your hand)" with a 'Hei', enabling us to read 'Yad Kehah' (the weak hand. Alternatively, we learn from the Hei at the end, a feminine form.)

Tana'im argue about this:

(Beraisa #1): "Yadchah" teaches that we wear the Shel Yad on the left hand.

Others say, "Yadcha(h)" includes a Gidem (one whose arm was cut off).

38a (Mishnah): Tefilin Shel Yad is not Me'akev the Shel Rosh, nor vice-versa.

(Rav Chisda): This is only if the person has both Tefilin. If he only has one of them, he cannot do the Mitzvah.

Rabanan: Did you really say that?

Rav Chisda: No. If one cannot do two Mitzvos, he should at least do one!

Question: What was Rav Chisda's original reasoning (before he retracted)?

Answer: He decreed lest one with only one Tefilah not strive to get the other.

Rishonim

Rif (Hilchos Tefilin (after Menachos) 8b): The Tefilin Shel Yad is not Me'akev the Shel Rosh, nor vice-versa.

Nimukei Yosef (DH Ein): If one encountered the Shel Rosh first, he puts it on first, lest he pass over a Mitzvah.

Rambam (Hilchos Tefilin 4:4): The Tefilin Shel Yad is not Me'akev the Shel Rosh, nor vice-versa, for each is a Mitzvah by itself.

Rosh (Hilchos Tefilin Siman 15): Whether or not one has both Tefilin, they are not Me'akev each other. If one can wear only one due to Ones, e.g. he must travel and he cannot delay to put on the Shel Yad, he puts on only the Shel Rosh. We are not concerned for 'whenever they are between your eyes, they must be two.'

Question (Magen Avraham OC 26:1): What is the source of this? Perhaps we permit only due to total Ones, e.g. a wound on his hand! It seems that when he will wear both later, the Rosh teaches that he may wear one now. See what I will write below in Siman 38:9.

Question (Eshel Avraham): Why should a delay permit an Isur Torah to put on the Shel Rosh first? What does the Magen Avraham bring from Siman 38? There, we exempt one who is in pain! Perhaps he compares delaying one's journey to pain. This requires investigation.

Answer #1 (Levushei Serad): Surely, a delay does not permit an Isur Torah! The Magen Avraham says that he cannot wear the Shel Yad now, e.g. due to traveling it would cause pain, e.g. due to the cold. Therefore, he is exempt from the Shel Yad, so we do not apply 'whenever they are between your eyes (they must be on your arm).' He proves from 38:9 that one who is in pain is exempt from Tefilin.

Note: In 39:11, the Magen Avraham cited the Yerushalmi, which says that R. Yochanan would not wear Tefilin due to the cold. I.e. he wore only the Shel Yad (like the Gra says). Likewise, we can say that here we discuss one from whom it is painful only to wear the Shel Yad, like Levushei Serad says.

Machatzis ha'Shekel: The Magen Avraham explains that the exemption is not due to distraction, for he says there (38:12) that one must settle his mind and wear Tefilin! The Magen Avraham questions the Rosh's source that a small Ones overrides the Isur to wear (now) the Shel Rosh without the Shel Yad. The Rosh must hold that this is not a severe Isur. The Nimukei Yosef holds that if one encountered the Shel Rosh first, he puts it on first, lest he pass over a Mitzvah. He must hold that the Isur of wearing the Shel Rosh without the Shel Yad is a light Isur. Even though we hold that if one encountered the Shel Rosh first, he puts it back and wears the Shel Yad first, we learn from the Nimukei Yosef that this is a light Isur.

Poskim

Shulchan Aruch (OC 26:1): If one has only one Tefilah (Shel Yad or Shel Rosh), or due to an Ones he can wear only one of them, he wears it and blesses on it.

Beis Yosef (DH v'Afilu): Surely, we hold like Rav Chisda's retraction. We do not decree about one who has only one Tefilah. Perush ha'Mishnayos (Menachos 4:1) is like his initial opinion. This is an errant Talmid's mistake that printers put in the text. It is not in the original Arabic. The Mishnah Torah says Stam that they are not Me'akev each other, i.e. whether or not he has both. The Rosh permits wearing just one, e.g. when there is Ones. Without Ones, one may not put on the Shel Rosh first, and surely he may not Mevatel either one. In any case, if he put on one, even if he has both, he was Yotzei that Mitzvah. Semak says that this is only if he has only one. If he has both, they are Me'akev. He cannot mean that he was not Yotzei. Rather, they are Me'akev, i.e. one may not wear only one.

Drishah (1): Rav Chisda initially held that the Mishnah says that they are not Me'akev each other only if he has both, but if not, we forbid him to wear even one, lest he be negligent and not get the other. The Beis Yosef says that even if he had both, but wore only one, he was Yotzei even if there was no Ones. There is no necessity to say so.

Beis Yosef (DH v'Yesh): The Tur says that they are not Me'akev even when he has both, i.e. this is the bigger Chidush. The Gemara brought a reason why they should be Me'akev when he has only one! I explain say that we hold like Rav Chisda's retraction, that there is no decree. It is more clear that they are not Me'akev when he has only one, for there is no reason not to do the one Mitzvah he can do. When he has both, perhaps they are like one Mitzvah!

Drishah (DH v'Chasav): This was not difficult. Rav Chisda initially held that when he has both they are not Me'akev, i.e. if now he cannot wear the other, but later he will. The Tur teaches about a case in which also later he cannot wear the other, e.g. he must travel. One might have thought that then, they are Me'akev. He teaches that they are not.

Mishnah Berurah (1): If one can wear only one, some say that it is better to wear the Shel Rosh, which is more Kodesh. Some say that he should not change the order, and should wear the Shel Yad. If he will not be able to wear both later, he may not travel until wearing both.

Kaf ha'Chayim (4): Mahari Molcho (81) permits one to wear only Shel Yad if he must pass among Nochrim who will mock him. I say that one should not refrain due to those who will mock him.

Ma'aseh Rav (Hilchos Tefilin 18, in Sidur ha'Gra): One may eat Arai (not in a fixed way) with Tefilin on. If one is concerned for haughtiness in front of others, he can wear only the Shel Yad. However, it is better to make a small Shel Rosh and cover the straps than to wear only the Shel Yad.

Shulchan Aruch (38:9): One who is in pain, or one whose mind is not settled, is exempt from Tefilin, because one may not take his mind off them.

Magen Avraham (11): This connotes that he is exempt even if he is pained by the cold, like it says in the Yerushalmi that R. Yochanan would not wear Tefilin due to the cold. There was one who would not wear Tefilin on the day he arrived from traveling.

Gra: The Yerushalmi says that R. Yochanan would wear both Tefilin in summer, but in winter, when his head hurt, he wore only the hand Tefilin.

Magen Avraham (12): He is exempt only if he cannot settle his mind.