In addition to washing our hands before eating bread, King Solomon instituted eiruvin to safeguard the sanctity of Shabbos. We commonly use the term “eiruv” to refer to the string around a community but there are many different types of eiruvin. Eiruvei chatzeiros enable the residents of a courtyard to carry in their common area on Shabbos. Analogous to this is shittuf mavuos, which applies to the residents of an alley. Eiruvei techumin enable people to shift the center of their Sabbath boundary so that they may travel further in one direction (albeit at the expense of the opposite direction). An eiruv tavshilin, when Shabbos occurs immediately after Yom Tov, allows one to continue his Sabbath food preparation over the Festival.
This mitzvah is the subject of the Talmudic tractate of Eiruvin. Eiruv tavshilin is discussed in the second chapter of tractate Beitza, starting on page 15b. The laws are codified in the Shulchan Aruch in Orach Chaim 366, 408 and 527.
While we call these the “7 Rabbinic Mitzvos,” that is just because these are the ones for which brachos were instituted, as we have said. There are, in reality, many rabbinic mitzvos. Tisha b’Av and the other fast days, for example, are just as “real” as Chanukah and Purim–the fasts are even discussed in Tanach in the seventh and eighth chapters of the Book of Zechariah. Similarly, Moshe and Ezra instituted the public reading of the Torah. While one says a bracha when receiving an aliyah, he does not recite a blessing “that God commanded us to read the Torah.” Rather, he recites a blessing on Torah study, which is a Biblical commandment.