I believe that the masked man robbed the bank. At the same time, I believe that my father did not rob the bank. Clearly, I can conceive that the masked man is not my father. Now, whoever the masked man is, it is impossible that he is someone else - if he is not my father then it's impossible that he is my father, and if he is my father then it is impossible that he is not. Father turns out to be the masked man who robbed the bank.