Do you think Elsa's will to protect Anna and her people during the night of the incident was strong enough to prevent her mind from snapping out of fear? 

I have a friend who's wondering whether or not Elsa had Dissociative Identity Disorder, and I tried to give him an answer, but I failed. I'm trying to give a solid answer, but his questions are just mind-boggling and tiresome. I don;t want to leave him in the dust because he's my friend, but I can't help him alone...I need an answer.
Will you please help me?