לע"נ מרדכי גימפל בן אברהם משה
The mishna at the beginning of maseches shabbos says that the melacha of hotzaa is המוציא מרשות לרשות.
What is the definition of hotzaa? Is it transferring from one domain to another "חילוף רשויות", as implied by the words המוציא מרשות לרשות. According to this understanding, in truth, if one transfers from one רשות היחיד to another רשות היחיד he should be liable. However, there is a גזירת הכתוב that one is only חייב if he transfers from רשות היחיד to רשות הרבים or vice versa because that is what happened in the mishkan. According to this we can understand the language of the Rambam הוצאה והכנסה מרשות לרשות מלאכה מאבות מלאכות היא, besides the fact that we see that הכנסה into the private domain is a melacha unlike the sugya 96b [see sfas emes דף ב], we also notice that the Rambam says "מלאכה" מאבות מלאכות "היא" - which is לשון יחיד. This indicates that the melacha is transferring from one domain to another and therefore it doesn't matter from which domain it is being transferred and transfers in both directions are subsumed under one single melacha.
There is another possibility: The melacha is carrying an object "נשיאת משא" yet there is a תנאי that this carrying must be from one domain to another. Based on this approach we can better understand the question of the gemara מרשות היחיד לרשות היחיד מאי קעביד ? If one transfers from one private domain to another - what did he do?! It DOESN'T say that he is פטור - it says that he did nothing. Based on our previous understanding the transfer from one רשות היחיד to another is significant [because the melacha is חילוף רשויות and logically he should be חייב] but he is nevertheless פטור [a special גזירת הכתוב because they didn't have it in the mishkan], so the gemara's question makes no sense.
However, based on our present understanding the question makes sense - the melacha is carrying an object from one place to another and there is a condition that it be from רשות היחיד to רשות הרבים or vice versa. If that is the case, the fact that the object went from רשות היחיד to רשות היחיד is meaningless, "מרשות היחיד לרשות היחיד מאי קעביד". The problem is that according to this second approach, the language of the mishna המוציא מרשות לרשות is problematic because that is not the definition of the melacha but merely it's תנאי.
Now see Tosfos and the Rambam and determine where they stand with regard to this חקירה.
[Based on the Sefer שעשועי תורה סימן א and see also the Dibros Moshe Simman Aleph anaf beis].