Exceptional syllogism does not mean exempting something from a rule in the everyday sense. It is a logical form in which a conditional or related premise is followed by another premise affirming or denying a part.
For example:
If Zayd is human, he is an animal.
But Zayd is human.
Therefore Zayd is an animal.
The inference succeeds because affirming the antecedent allows the consequent to follow, assuming the conditional is true.