I've come across phrases like this a couple of times where でいる is used right after a noun instead of the usual Te-form verb + いる:
どうせ学生でいるなら一番でいたいし
In this case is it basically just the same as である?
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いる means to stay and で いる means to remain something or to keep being something.
It's different from である in the point that でいる implies that one is in that state for a certain period of time and no longer so when it's expired.
