[Avodah] irui k'li sheini

[Sholom Simon]

 The Biur Halacha holds that irui k'li sheini can cook kalei habishul -- if
the water is yad soledes bo (if lower than yad soledes bo, then he's not
sure)

RSZA holds that a k’li shlishi has the same status as irui k’li sheini, and
therefore one may not put an egg, tea leaves, halei habishul, etc. into it
as long as it is yad soledes bo.  (So, use tea essence to make tea, e.g.)

RMF holds that a k'li shlishli doesn't cook anything.  (You don't need tea
essence).  My understanding is that the Yalkut Yosef also permits
everything in a k’li shlishi.

My question is: where does RMF (and/or ROY) stand on irui k'li sheini?
*If* he holds, like RSZA, that  that a k’li shlishi has the same status as
irui k’li sheini, then he would hold that an irui k’li sheini doesn't
cook.  But that would be against the Biur Halacha.  It would seem that the
only other option is that he agrees with the Biur Halacha (that irui k'li
sheini cooks) but disagrees with RSZA (that they don't have the same
status), and therefore RMF would hold that: "yes, al pi the Biur Halacha,
irui k'li sheini can cook, but contra RSZA a k'li shlishi never cooks."

Am I thinking this through correctly?

Thoughts?

Thanks,

-- Sholom
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