Your proof is a bit poor. Logically your statement means: "It is not the case that I'm going nowhere". "I'm going nowhere" can be paraphrased as "I'm not going anywhere". If it is put under negation we get "It is not the case that I'm not going anywhere". Now, this implies going somewhere.
We may not be talking about standard English. If we were to take AAVE (African American Vernacular English) into account for example, it would, indeed mean "I'm not going anywhere"
saber
