It's been a while since I learned formal logic. My best guess:
Saying "all things die" is the same as saying "nothing exists that does not die."
"Not" is being used both formally and as part of a title. I'd rewrite the right half of the equation as "Not (Exist x : NotDie x)" to remove that ambiguity.
Also, my interpretation is based in part on a desire to avoid figuring out how to formally state Not Exist X in terms of existential and universal quantifiers.
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