Who Stole What from Whom? (Who Stole What from Whom? Part X)

(N.b. my reasoning differs from that in the solution presented by the author substantially, yet we reach the same conclusion. I am not sure the solution is airtight but it seems pretty solid so I am posting it here anyway.)

“And now, we come to a particularly good puzzle,” I said to the group proudly.
“Three girls—Abigail, Bernice, and Carol—each had a pet; one was a dog, one a cat, and the other a horse, but we are not told which girl owned which pet. One day, our three villains—Mike, Spike, and Slug—each stole a pet from one of the girls, but it was not known who stole what from whom. The case proved extremely baffling, but, fortunately, Inspector Craig of Scotland Yard was visiting the country at the time...”
“Who is Inspector Craig?” asked Barry.
“He is a character from one of my books,” I replied.
“What is the name of this book?” asked Barry.
“You just guessed it!” I said.
“Whatever do you mean?” asked Barry in astonishment.
“I mean just what I said; its name is What Is the Name of This Book?”
“Stop kidding us!” said Barry.
“He’s not kidding!” said Alice. “I’ve read the book, and its title really is What Is the Name of This Book?, and it really does contain a whole chapter of cases from the files of Inspector Craig.”
“Anyway,” I intervened, “Inspector Craig was able to find out the following facts, which were enough to solve the case.

1. The one who stole the horse is a bachelor and is the most dangerous thief of the three.
2. Abigail is younger than the girl who owns the dog.
3. Mike’s brother-in-law, Slug, who stole from the eldest of the three girls, is less dangerous than the one who stole the dog.
4. The man who stole from Abigail is an only child.
5. Mike did not steal from Bernice.

Who stole what from whom?”

(Source: King Arthur in Search of His Dog and Other Curious Puzzles by Raymond Smullyan)

Slug is revealed to be the brother-in-law of Mike, which means that Mike is married and is therefore not a bachelor and is therefore neither the horse-thief nor the most dangerous of the three. Additionally, Slug has been described as "less dangerous" than one of the other thieves, which leaves only Spike to be the horse-thief.

Since the horse is now (partially) accounted for, it should be pointed out that Slug is compared as "less dangerous" to the one who stole the dog. This leaves only the dog to be stolen by him. And it also means that Mike stole the dog. So far, so good; who stole which pet is already fully accounted for.

Slug (the cat-thief) stole from the eldest of the three girls. Since Abigail is described as younger than the girl who owns the dog these facts mean jointly that she must own the horse.

With the horse now fully accounted for, the fact that Mike (the dog-thief) did not steal from Bernice means that Bernice owns the cat. With only one pet left, Carol must own the dog.

Final answer: Mike stole the dog from Carol; Spike, the horse from Abigail; and Slug, the cat from Bernice.