Retaining deposit after terminating with cause

[Account Closed]

Rented to a man with one dog. After it turned into man, woman, 5 dogs, 3 cats, and rent paid apx 30 days late every month, I served a 10 day notice under the basis of terminating with cause. They did leave within 10 days. 

I'm looking to confirm if I can still keep the security deposit under the pretense that I lost rent as a result of their actions. Even if I had wanted to show the place after having given notice, I couldn't reasonably do so. Their dogs were aggressive and the apartment was filthy and smelled strongly of cat urine. 

As much as it makes sense to me, I'm well aware I'm not the law. Any thoughts from other landlords who prefer to stay out of court?

[Nathan Gesner]

Why they left doesn't really matter. The security deposit can typically be applied towards cleaning and repairs. I suspect you could easily spend the deposit on cleaning, deodorizing, or even replacing the flooring.