I am not sure how to define if a Mitzvah is from Rabanan or Torah. For example: According to Berachot daf 21, Chazal learned from Kal Vachoner that Beracha before eating is from Torah, although the Torah does not write it BeFeirush. In this case, when Chazal learned, would it be Mitzvah DeRabanan? or from DeOrayta? Another example is "Tuma'at Of Tahor" it does not say BeFeirush in the Torah.
Is there any different in the applications between those that were written Beferush in the Torah to those that were leaned by Chazal?
Aaron Gal, Fair Lawn, New Jersey USA
Generally speaking, whatever is learned from a 'Kal va'Chomer' (or from any of the thirteen Midos of Rebbi Yishmael) is d'Oraisa. Consequently, had the Gemara not refuted the Kal va'Chomer, Berachos before eating would be Min ha'Torah.
Likewise, the Tum'ah of Nivlas Of Tahor (which is what I assume you are referring to) is Min ha'Torah, seeing as the Chachamim derive it from the wording of the Pasuk, even though it is not written be'Feirush. I believe that, at times, there are slight differences between something that is mentioned be'Feirush in the Torah and something that is only learned from a Limud, but to all intents and purposes, the answer to your last question is 'No, there is not!'
Having said that, one must also bear in mind that Chazal often support their own laws and decrees with a Pasuk. This is known as an 'Asmachta', and, in spite of the Pasuk that they quote, it is only mid'Rabanan. Rashi normally points out when a particular Limud is only an Asmachta.
Be'Virchas Kol Tuv
Thank you for your reply. If you don't mind me further asking...
My objection to the kal vechomers is that doesn't something have to be absolutely kal and absolutely chamur for one to make the kal vechomer? How can you learn a kula in one area each and a chumra in one area each? In that case, even though the kal vechomers might work separately, together neither Mazon or Torah is kal or chamur?
Also, if I may ask some [seemingly weak] questions, even though I guess this will be easy for you to answer: if the Rashi is like you're saying,
1) Why would we think that the Gemara is talking about anything other than d'Oraisa brachot? D'oraisa is seemingly the whole discussion here?
2) Why does Rashi then need to comment specifically on the words 'ta'un leachrav' and quote that passuk? Seemingly that is superfluous?
Kal v'Chomer's are often used in one specific area. When we find an obligation regarding one aspect of a law, and that same aspect of another law is not specified but would seemingly present a stronger case for obligation than the same aspect of the first law, we have the beginnings of a Kal v'Chomer. Accordingly, one could technically derive a Kal v'Chomer from two different laws to each other, as long as the aspects of those laws follow a Kal v'Chomer process.
Of course, there could be reason to have a Pircha on these Kal v'Chomer's, by bringing a second aspect of the first law, such as punishment for its transgression, which is far more stringent than the second law. However, if there is no significant difference between the two laws, even if there is a slight difference, a Kal v'Chomer can address one aspect of each law, as explained above (see Halichos Olam Sha'ar Revi'i, 2:6). In this fashion, a Kal v'Chomer can be derived two ways.
1) The common way to learn this Gemara is based on Tosfos (35a), that this Kal v'Chomer in general is actually mid'Rabanan, as Berachos before food are mid'Rabanan. If this is how Rashi is learning, it would make perfect sense why he would comment that there is no explicit Pasuk for this. He means that while Berachos still have to be made mid'Rabanan, they do not have to be made according to Torah law. Rashi might also have used this terminology to address the famous question of how Berachos can be a "Sevara" and yet mid'Rabanan. [Although the Pnei Yehoshua here argues, and of course one could maintain that Rashi holds like the Pnei Yehoshua's approach, this is the standard way of understanding the obligation of a Berachah Rishonah.]
2) Nope. He is merely saying that Rebbi Yochanan agrees to Rav Yehudah quoted above that this is the source of the teaching.
I am not saying that there is no other explanation, but I do think this is a simple explanation of Rashi.
All the best,