פירוש על מנחות 4:1

התכלת אינה מעכבת את הלבן – although it is a Mitzvah to place two threads of Tekhelet/blue and two threads of white or one thread of Tekhelet and three threads of white, nevertheless, this does not impair/invalidate by omission the other, and if he placed all four of them with Tekhelet or all four of them with white [threads], he has fulfilled his religious obligation.

Introduction In this mishnah we learn of cases where the absence of a part of a certain mitzvah does not prevent the fulfillment of the whole mitzvah.

תפלה של יד אינה מעכבת של ראש – Maimonides wrote, specifically that both (i.e., the Tefillin of the hand and the Tefillin of the head) are found with him. But only one of them is found with him, he should not put on the one until he has found the other since we make a decree lest he error and rely always on the one [only]. But this is not according to the Halakha, for the one who says this in the Gemara (Tractate Menahot 44a) retracted based upon the strength of what he was questioned but rather one who does not have [in order to fulfill] the two commandments, he should not even observe the one commandment, is to be read as a question [in astonishment]! But the Halakha is that whether both (i.e., the Tefillin of the arm and Tefillin of the head are found with him or whether they are not found with him, they do not impair/invalidate by omission the other, and so have admitted all of my teachers/Rabbis that this is the Halakhic practice.

The [absence of the] blue [in the tzitzit] does not invalidate the white, neither does the [absence of the] white invalidate the blue. Tzitzit consist of white and blue strands (Numbers 15:38). If one makes tzitzit with only white or only blue strands, he has fulfilled the mitzvah. Today most people wear tzitzit with only white threads because for many years rabbis did not know how to make the blue threads. However, recently people re-discovered how the blue threads were made. Nowadays, it is becoming increasingly more common to see people with tzitzit made of blue and white.

הסולת והשמן – of the libations of the meal-offering.

The [absence of the] hand-tefillin does not invalidate the head-tefillin, neither does the [absence of the] head-tefillin invalidate the hand-tefillin. Tefillin are worn on the head and arm. These are two separate mitzvoth, so if a person wears one and not the other, he has fulfilled the mitzvah of wearing that particular piece of tefillin.

אין מעכבין את היין – of the libations that if they brought the wine without the fine flour and the oil, he offers as a libation.

The [absence of the] fine flour and the oil does not invalidate the wine, neither does the [absence of the] wine invalidate them. A minhah that is accompanied by libations comes with three elements: flour, oil and wine. If one offers one or two of these elements, but not the others, he has fulfilled the mitzvah of that which he offered.

המתנות של מזבח החיצון – as, for example, the four gifts of the sin-offering.

The [omission of one of the] sprinklings [of the blood] on the outer altar does not invalidate the rest. Some sacrifices require the blood of the animal to be sprinkled on the outer altar, either four times or twice (see Zevahim 5:3-7). If he omits one of the sprinklings he has still fulfilled the mitzvah (see Zevahim 4:1).

אין מעכבות זו את זו – that if he did not give other than one [of them], he has atoned, as it is written (Deuteronomy 12:27): “the blood shall be poured out [on the altar of the LORD your God],” that one pouring/spilling is implied.