Dedicate Daf 29b to:

מטבול יום דשרץ
From a Tevul Yom
(who became impure after touching)
a rodent
(And was never an Av.)

And if a Tevul Yom can make a Sheini, all the more so a Sheini should make a Shelishi.
מה לטבול יום דשרץ שכן במינו אב הטומאה
On the other hand, even a
Tevul Yom
after touching a rodent may be stricter than a Sheini
there are other Tevul Yoms (such as one who touched a corpse) which can make a human or vessel an
Av HaTumah.

And food (which is the only thing (along with drink) which can become a Sheini) can never become an Av, so there is no Kal Vachomer .
The Gemara tries again:
כלי חרש יוכיח
An earthenware vessel
(which can make Terumah into a Sheini)
will prove
that a non-sanctified loaf can make Terumah into a Shelishi,

An earthenware vessel, which can make food into a Rishon, can never itself become an Av HaTumah (like food and unlike people). So the Gemara can use the above logical inference to prove that a Sheini make other food into a Shelishi.
The Gemara answers:
מה לכלי חרש שכן מטמא מאוירו
on the other hand,
earthenware vessel's
impurity is stronger than regular "food impurity" as it can make other objects impure through its

While most impurities are transferred through touching (something can become impure only by touching another source of impurity), earthenware vessels can become impure (and make other objects impure) just by being within its airspace (So if one dangled a rodent into a jug, the jug is impure even if the rodent didn't touch anything).
So one cannot derive a Kal VaChomer from an earthenware jug to other (food) impurities.
The Gemara will try another proof:
טבול יום יוכיח
A Tevul Yom can prove
that a non-sanctified loaf can make Terumah into a Shelishi,

As mentioned on page .
Even though the Gemara previously disproved (on page
) this Kal VaChomer , the Gemara continues:
וחוזר הדין
And this proof goes back on itself,

לא ראי זה כראי זה ולא ראי זה כראי זה
Each proof has faults different than the other

הצד השוה שבהן שמותרין בחולין ופוסלין בתרומה
But the common denominator
between a Tevul Yom and an earthenware jug
is that they make Terumah impure
even though
they are
permitted with non-sanctified products themselves.

What causes the earthenware jug and Tevul Yom to make food into a Sheini? It must be the common denominator - they're both Tamei. So anything Tamei (even if it doesn't have any special stringencies of the earthenware jug or the Tevul Yom ) can make a Shelishi.
כל שכן ככר שני שפוסל בחולין דפוסל בתרומה
All the more so a Sheini loaf
which makes a non-sanctified loaf Pasul
should make Terumah
into a Shelishi

This is the source of the law that Terumah can become a Shelishi.
Now, the Gemara will explain the reason the "future generations" will argue:
ודור אחר פריך
But the future generation will ask
on this Kal VaChomer :

The says that the only common denominator between the earthenware jug and the Tevul Yom is that they're both impure. However, the Gemara says that...
מה להצד השוה שבהן שכן יש בהן צד חמור
common denominator - they are both are strict
(though in different ways).

So one can't use the lack of a common denominator to show that
impure object can make a Shelishi, for there is another common denominator - that they are unique.
So the Gemara asks why don't we consider Shelishi Terumah impure?
The Gemara answers:
ורבן יוחנן בן זכאי צד חמור לא פריך
But Rabbi Yochanan ben Zakkai says that "they're both strict" is not a
common denominator

So he holds that Terumah may become a Shelishi.
The Gemara now discusses the source that sanctified food can become a Reviyi:
There are two opinions:
A Braisa was taught:

אמר רבי יוסי
Rabbi Yossi said:

מנין לרביעי בקודש שפסול
What is the source that a sanctified object can become a Reviyi?

As mentioned , Terumah and non-sanctified foods may, at most, become a Shelishi.
Rabbi Yossi proves how sanctified objects can achieve a fourth level of impurity:
ודין הוא
It is a logical inference:

מה מחוסר כיפורים שמותר בתרומה פסול בקודש שלישי שפסול בתרומה אינו דין הוא שיעשה רביעי בקודש
If a Mechusar Kippurim ,
(who is technically pure)
is permitted to eat Terumah but
makes sanctified foods impure, all the more so should a Shelishi, which makes Terumah impure, make sanctified foods into a Reviyi.

ולמדנו שלישי לקודש מן התורה ורביעי מקל וחומר
So the source that sanctified
food can become
a Shelishi is
biblical, while the source that
sanctified foods can become a Reviyi
is logic.

שלישי לקודש מן התורה מנלן
What is the source that sanctified foods can become a Shelishi?

דכתיב והבשר אשר יגע בכל טמא לא יאכל
The verse says
"And the flesh that touches any impure thing shall not be eaten,"

מי לא עסקינן דנגע בשני
the verse
not mean that the
touched a Sheini?

ואמר רחמנא לא יאכל
despite that,
the verse says that
this Shelishi
cannot be eaten.

רביעי מקל וחומר כדאמרן
And the logical inference was said .

אמר ר' יוחנן טעם בריבי איני יודע מה הוא שהרי תשובתו בצדו
Rabbi Yochanan,
on the other hand, says
that he does not understand the reasoning of
Rabbi Yossi
, as the disproof
of his Kal VaChomer
is right next
to the proof

אוכל הבא מחמת טבול יום יוכיח שפסול בתרומה ואינו עושה רביעי בקודש
food touched by a Tevul Yom , which makes Terumah impure, does not make
even sanctified foods a

Rabbi Yochanan reasons that Rabbi Yossi follows the opinion of , who say that a Tevul Yom (which is parallel to a Sheini) is only strong enough to make sanctified food impure directly, but not through an intermediary (which is parallel to a Shelishi).
However, according to Rabbi Yossi's inference, a Tevul Yom
be strong enough to make sanctified foods impure even through a proxy (making a Reviyi from a Tevul Yom ), since if a Mechusar Kippurim (which is weaker than a Sheini) can makes Terumah impure (as a Shelishi), all the more so should a Tevul Yom (which is stronger than a Mechusar Kippurim ) make sanctified foods into a Reviyi.
The Gemara will now prove that a Tevul Yom cannot make a Reviyi:
The Gemara cites three opinions regarding how many levels of impurity can a Tevul Yom go:
As a Braisa taught:

אבא שאול אומר טבול יום תחילה לקודש לטמא שנים ולפסול אחד
Abba Shaul said that
the Rabbis decreed that
a Tevul Yom
can be
a Rishon
foods, (so it can start a three-level chain of impurity),

ר' מאיר אומר מטמא אחד ופוסל אחד
Rabbi Meir
said that a Tevul Yom starts a two level chain of impurity,

וחכמים אומרים כשם שפוסל אוכלי תרומה ומשקי תרומה כך פוסל אוכלי קודש ומשקי קודש
While the Sages said that just as
a Tevul Yom makes
the eater of Terumah impure
(but not the food), so too a Tevul Yom makes
the eater of sanctified foods impure
(but not the food).

The Gemara responds:
מתקיף לה רב פפא ממאי דר' יוסי כרבנן סבירא ליה דילמא כאבא שאול ס"ל דאמר לטמא שנים ולפסול אחד
Rav Papa asked, how do we know that Rabbi Yossi agrees with the Sages, perhaps he follows Abba Shaul who said
that a Tevul Yom starts a three level chain of impurity?

Rabbi Yochanan's disproof of Rabbi Yossi depends on Rabbi Yossi agreeing with the Sages.
If Rabbi Yossi agrees with Abba Shaul, who says that a Tevul Yom starts a chain of impurity, then his opinion makes sense, as a Tevul Yom
strong enough to make sanctified foods impure through a proxy.
The Gemara answers:
אי סלקא דעתך כאבא שאול ס"ל לייתיה לרביעי בקודש מאוכל שבא מחמת טבול יום
Rabbi Yossi
followed Abba Shaul's
, he would have derived that sanctified
foods can become a Reviyi
the law of
food the touched a Tevul Yom
(rather than from the Mechusar Kippurim ).

As follows:
ומה אוכל הבא מחמת טבול יום דטבול יום גופיה מותר בחולין אמרת עושה רביעי בקודש
If food which touched a Tevul Yom
who is permitted to eat non-sanctified food
) is strong enough to
make sanctified food into a Reviyi,


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