Is ADHD and Anxiety considered a mental illness for legal purposes?

I was considering applying for a concealed weapons permit.

"The applicant does not have a diagnosed mental illness at the time the application is made regardless of whether he or she is receiving treatment."

I was diagnosed with ADHD and anxiety two years ago by a psychiatrist. I stopped going to the psychiatrist after realizing my concentration problems were due to anxiety. I no longer have anxiety problems.

Is anxiety disorder a mental illness? Will these two diagnoses hold me back in life?

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