Troubleshooting Exporting Events with Undefined User Emails in Mixpanel

speaking of exporting events, I'm looking at exporting events where the user's email is not defined and I tried the following selector strings:

not defined(user["$email"])

and

user["$email"] == undefined

but they both result in HTTP 400 Error: Bad Request Similar requests work if I replace user with properties. Am I reading the docs wrong or something? https://developer.mixpanel.com/reference/segmentation-expressions