Here is the argument:

1. No N is not-N.

2. No not-N is N.

3. All C are N.

4. No R are C.

Thus: No R are N.

The syllogism is invalid for two reasons. First, the third premise denies the antecedent (cats) of the fourth. There can be other animals that are normal. Wikipedia: Denying the antecedent; Formal fallacy.

Second, a term that is distributed in the conclusion (normal) is not distributed in the major premise (all cats are normal). Wikipedia: Illicit major.

The first two premises are not needed except as definitions. The second two, about cats and rabbits, state actual relationships between categories,

Here is the argument:

1. No N is not-N.

2. No not-N is N.

3. All C are N.

4. No R are C.

Thus: No R are N.

The syllogism is invalid for two reasons. First, the third premise denies the antecedent (cats) of the fourth. There can be other animals that are normal. Wikipedia: Denying the antecedent; Formal fallacy.

Second, a term that is distributed in the conclusion (normal) is not distributed in the major premise (all cats are normal). Wikipedia: Illicit major.

The first two premises are not needed except as definitions. The second two, about cats and rabbits, state actual relationships between categories,