Illicit minor is a logical fallacy committed in a categorical syllogism that is invalid

Validity

In logic, argument is valid if and only if its conclusion is entailed by its premises, a formula is valid if and only if it is true under every interpretation, and an argument form is valid if and only if every argument of that logical form is valid....

 because its minor term

Minor term

The minor term is the subject term of the conclusion of a categorical syllogism. It also appears in the minor premise together with the middle term. Along with the major term it is one of the two end terms.Example:...

 is undistributed in the minor premise but distributed in the conclusion.

This fallacy has the following argument form:

All A are B.

All A are C.

Therefore, all C are B.

Example:

All cats are felines.

All cats are mammals.

Therefore, all mammals are felines.

The minor term here is mammal

Mammal

Mammals are members of a class of air-breathing vertebrate animals characterised by the possession of endothermy, hair, three middle ear bones, and mammary glands functional in mothers with young...

, which is not distributed in the minor premise "All cats are mammals," because this premise is only defining a property of possibly some mammals (i.e., that they're cat

Cat

The cat , also known as the domestic cat or housecat to distinguish it from other felids and felines, is a small, usually furry, domesticated, carnivorous mammal that is valued by humans for its companionship and for its ability to hunt vermin and household pests...

s.) However, in the conclusion "All mammals are felines," mammal is distributed (it is talking about all mammals being felines). It is shown to be false by any mammal

Mammal

Mammals are members of a class of air-breathing vertebrate animals characterised by the possession of endothermy, hair, three middle ear bones, and mammary glands functional in mothers with young...

 that is not a feline

Felidae

Felidae is the biological family of the cats; a member of this family is called a felid. Felids are the strictest carnivores of the thirteen terrestrial families in the order Carnivora, although the three families of marine mammals comprising the superfamily pinnipedia are as carnivorous as the...

; for example, a dog

Dog

The domestic dog is a domesticated form of the gray wolf, a member of the Canidae family of the order Carnivora. The term is used for both feral and pet varieties. The dog may have been the first animal to be domesticated, and has been the most widely kept working, hunting, and companion animal in...

.

Example:

Pie is good.

Pie is unhealthy.

Thus, all good things are unhealthy.