Can someone be diagnosed with anorexia and bulimia simultaneously?

According to the DSM-5 if you binge and purge during an episode of anorexia nervosa, you're diagnosed with anorexia binge-purge type and not with bulimia.

But what about the ICD-10? Where anorexia binge-purge type (in the DSM) is actually traduced to bulimia according to the ICD?

Then you simultaneously have anorexia (DSM) and bulimia (ICD). Am I wrong?

I'm not a professional that's why I need validation and confirmation.