Zevachim 79: Combining Mitzvot of Similar/Different Levels - the Case of the Hillel Sandwich

Among the secondary examples including cleaning the urine of a zav/ah and using the damp flax spun by a woman who is niddah, today's daf teaches us the roots of a familiar tradition regarding combining of different types. 

The example is taken from the hagadah, where we eat matza and maror together.  We use the blessings of "ha motzi"; "al achilat matza" on the matzah, and "al achilat maror" over the maror.  We also recite the blessing of "borei pri ha adama" over the karpas, and then we eat the matza and maror together in what we call a "Hillel Sanwich". 

Massechet Pesachim (115) teaches us that Hillel believed that two mitzvot done together do not nullify each other.  There would be no need to combine or separate the mitzvot to eat matza and maror together.  Hillel uses the proof text found in Bamidbar (9:11) that states that the korban pesach, the paschal lamb, or the Passover sacrifice, will be eaten together with the matzah and the maror.   This is agreed upon by the Sages in Masechet Pesachim, but they do not consider it to be necessary.  The Talmud Yeurshalmi suggests that if there are three mitzvot done at the same time, the first two overwhelm the third. 

According to our Gemara, two mitzvot must be at the same level to avoid nullifying each other.  For example, both would have to be Biblically derived.  If one of the mitzvot is at only a rabbinical level, it would be ruled that they cannot be performed together or at the same time.  Steinsaltz explains that since the destruction of the Temple, there are no sacrifices.  In particular, there is no korban pesach.  Thus taking maror is a rabbinic mitvah and we can no longer eat matza and maror together.

As we know, our current practice involves first blessing and eating maror and matza separately, followed by eating them together in remembrance of Hillel's ruling.  The Jerusalem Talmud is clear regarding the combining of mitzvot - a rabbinic mitzvah cannot override a biblical mitzvah.  The disagreement regarding Biblical mitzvot that overlap each other still holds.