Dedicate Daf 29a to:

שהרי עשה בה ספק זונה כזונה
the Torah
that the laws of a
doubtful harlot are the same as a

So just as a harlot is forbidden to marry her adulterer, so to is a doubtful harlot forbidden to her suspected adulterer.
The Gemara rejects this, for:
תרומה נמי לא תיבעי קרא שהרי עשה בה ספק זונה כזונה
Terumah also shouldn't need a verse, as
the Torah
that the laws of a
doubtful harlot
eating Terumah
are the same as
those of

Just as the Torah shouldn't need to explicitly write that a doubtful harlot is forbidden to a Kohen, the Torah shouldn't need to explicitly write that a doubtful harlot is forbidden to eat Terumah.
The Gemara answers:
אלא לר' עקיבא ארבעה קראי כתיבי
Rather, Rabbi Akiva expounds

Two "she's impure", a "and she's impure", and (as Rabbi Akiva the extra Vavs), the "and" adds a fourth verse.
חד לבעל
Teaches that a doubtful Sotah may not stay married to her

וחד לבועל
Teaches that a doubtful Sotah may not marry her suspected

וחד לכהונה
Teaches that a doubtful Sotah may not marry a

וחד לתרומה
Teaches that a doubtful Sotah may not eat

And Rabbi Yishmael comments (on page
) on the last point (Terumah).
ורבי ישמעאל תלתא קראי כתיבי
While Rabbi Yishmael
three verses:

The same as , but as he doesn't expound Vavs, he needs to expound the law that a suspected Sotah may not eat Terumah from a logical inference.
חד לבעל
Teaches that a doubtful Sotah may not stay married to her

וחד לבועל
Teaches that a doubtful Sotah may not marry her suspected

וחד לתרומה
Teaches that a doubtful Sotah may not stay married to her

וכהונה אתיא בקל וחומר
And the prohibition of Sotah to marry
a Kohen
can be derived from
a logical inference.

As the Gemara expounds above on page .
The Gemara asks on Rabbi Yishmael:
ורבי ישמעאל ממאי דאיצטריך קרא לתרומה וכהונה אתיא בקל וחומר
How does Rabbi Yishmael
that the verse
prohibits the Sotah
to eat Terumah and
that the prohibition of the Sotah marrying
a Kohen
is derived from a logical inference

דילמא כי אצטריך לכהונה ותרומה שרי
the verse only teaches that the Sotah is prohibited
a Kohen, while
she is permitted
to eat Terumah!

All we know is that something is prohibited, and the Sotah's prohibition to marry a Kohen is stricter than her prohibition to eat Terumah. So instead of saying that the verse teaches the lenient law (and then extend it to the stricter law), why not say that it prohibits only the stricter law?
The Gemara answers:
אמר לך מסתברא דומיא דבעל ובועל
Rabbi Yishmael
answers that
the prohibition mentioned in the verse is
similar to
the prohibition between the suspected wife and her
and between her
and her adulterer.

And as only Terumah is prohibited during the husbands lifetime, the verse must be prohibiting the Sotah from eating Terumah...
מה בעל ובועל מחיים אף תרומה נמי מחיים
Just as the husband and adulterer are forbidden
to a suspected Sotah
even during her
lifetime, so is Terumah forbidden to her
even during her husband's

לאפוקי כהונה דלאחר מיתה
the Sotah's prohibition against marrying a
is applicable only
after her husband's passing.

The only way a Sotah (who is married) can potentially marry anyone else is either through divorce or death of her husband.
If she's divorced, she is forbidden to another Kohen as a divorcee, and not as a Sotah. The only way she'll be forbidden to another Kohen due to her status as a suspected Sotah is if her husband passed away.
In contrast, she may continue to eat Terumah after a divorce even if the husband is still alive.
The Gemara will explain the two answers why doesn't Rabbi Akiva derive the prohibition of a Sotah eating Terumah this way (and uses the extra Vavs instead):
ור"ע דומיא דבעל ובועל לית ליה
Rabbi Akiva,
on the other hand
, doesn't agree
that there has to be a comparison between the "third prohibition" and the prohibition against
her husband and adulterer.

So according to Rabbi Akiva, we would expound the "third prohibition" not as prohibiting the Sotah from eating Terumah but prohibiting her from marrying a Kohen, and there would be no source that she's forbidden to eat Terumah (He doesn't hold of Rabbi Yishmael's rule ).
ואי נמי אית ליה מילתא דאתיא בקל וחומר טרח וכתב לה קרא
2. Another answer is that
the verse will
a law explicitly, even though it
can be derived through a Kal Vachomer .

So there is technically no need for the extra Vavs.
The Gemara asks:
The Gemara above (on page
) says that the source that an item who's purity is in doubt must be considered impure is the comparison with a Sotah. The Gemara now cites another source:
אמר רב גידל אמר רב דבר שיש בו דעת לישאל ואין בו דעת לישאל מהאי קרא נפקא
Rav Gidel asked in the name of Rav if the
law that a doubtful impurity in a private domain is impure only if
it can be " close
See page ( )
asked " derived from this verse?

והבשר אשר יגע בכל טמא לא יאכל
It is derived from
"And the flesh that touches any impure thing shall not be eaten,
it shall be consumed in fire. As for other flesh, only he who is clean may eat such flesh.

There is a contradiction in this verse (which discusses sacrificial meat):
ודאי טמא הוא דלא יאכל הא ספק טמא וספק טהור יאכל
The first part of the verse implies that meat
which is
impure may not be eaten, but
may be eaten.

אימא סיפא והבשר כל טהור יאכל
But the end
of the verse implies the opposite, as it says
"And as for the flesh, every flesh that is clean may be eaten thereof."

בשר ודאי טהור הוא דיאכל בשר הא ספק טמא וספק טהור לא יאכל
This, second, part of the above verse implies
pure meat may be eaten, but
may not be eaten.

So may one eat sacrificial meat which is doubtfully impure or not?
The Gemara resolves:
אלא לאו שמע מינה כאן שיש בו דעת לישאל כאן שאין בו דעת לישאל
The resolution is that the first part of the verse refers to
the impure item
can be "asked", while
the second part
refers to
where the impure item
which cannot be "asked".

So there's no need to prove it from the law of the Sotah.
The Rav answers:
ואיצטריך דרב גידל אמר רב ואיצטריך למיגמר מסוטה
One needs
the derivation
of both and from
the laws
of Sotah,

דאי מדרב הוה אמינא בין ברשות היחיד ובין ברשות הרבים איצטריך למיגמר מסוטה
Rav Gidel in the name of
derivation doesn't differentiate
between a private domain or a public domain.

ואי מסוטה הוה אמינא עד דאיכא דעת נוגע ומגיע צריכא
if one would derive that there are two laws of "doubtfully impure meat" only from the laws of
Sotah, one would think that both
the originally impure object
and the touched object need consciousness.

As in the Sotah's parallel case, both the adulterer and the wife have consciousness, while in the case of the meat, only the meat has consciousness.
: בו ביום דרש רבי עקיבא וכל כלי חרש כו':
On that day, Rabbi Akiva expounded "and all earthenware pottery"

The Gemara asks:
ומאחר דאין לו למה טמא
Why, if he doesn't
have a source, does Rabbi Yochanan ben Zakkai say that a Sheini can make Terumah into a Shelishi

The Gemara answers:
אמר רב יהודה אמר רב מן התורה אין לו מדין קל וחומר יש לו
Rav Yehuda said in the name of Rav, that while there is no
biblical source, there
is a
logical inference.

As follows:
ומה טבול יום שמותר בחולין פוסל בתרומה
If a Tevul Yom
who is permitted to eat not-sanctified foods
and Maaser)
makes Terumah Pasul
(A Sheini)

ככר שני שפסול בחולין אינו דין שיעשה שלישי בתרומה
All the more so should a Sheini
which is Pasul even if not sanctified
make Terumah a Shelishi.

The Gemara asks:
איכא למיפרך
One can disprove
that Kal Vachomer :

מה לטבול יום שכן אב הטומאה
Tevul Yoms
an Av.

The original proof depends on the principle that a Tevul Yom is weaker than a Sheini. The Gemara answers that a Tevul Yom could actually be more strict, as a Zav or Metzora who went to Mikvah is a Tevul Yom , but a Zav or Metzora can never be a Sheini (as only food and drink can become a Rishon or Sheini).
So the Gemara tries a different angle:
that a Sheini can make a Shelishi

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