There is a line said before donning the tzitzit, talit and the tefillin, and the shaking of the lulav which reads (text adapted from https://en.wikipedia.org/wiki/List_of_Jewish_prayers_and_blessings and I don't know if there are variants and translation from the Artscroll siddur)
יהי רצון מלפניך ה׳ א‑להי וא‑להי אבותי, שתהא חשובה מצות _____ לפניך כאלו קימתיה בכל פרטיה ודקדוקי וכונותיה ותריג מצות התלוים בה, אמן סלה.
May it be Your will, Hashem, my God and he God of my forefathers, the commandment of ______ be as worthy before You as if I had fulfilled it in all details, implications, and intentions, as well as the six hundred thirteen commandments that are dependent upon it. Amen, Selah!
In what sense are the taryag mitzvot dependent on the putting on of tallit, tzitzit and tefillin or shaking the lulav?
Note -- I don't know if the same formulation is said before the performance of other mitzvot but maybe knowing "why" there is dependence might help me anticipate other situations in which it is said or why it isn't.