Well, as I'm writing a definition, I can't exactly use a sentence, but I think I see your point. So to clarify, here are the two contexts I'm looking at.
intrinsic (adj.) = essentially part of something
intrinsic (adj.) = essential part of something
I don't like the second definition, because the word "part" is being use as a noun, and I am defining an adjective.
So in the first definition, I am curious to know whether the word "part" or the phrase "part of" is being used incorrectly, and if not, how would you explain its use?