Accused of theft at work by a coworker, no evidence. Employment terminated.

I work in security and was recently fired because one of my coworkers falsely accused me of stealing something from the building management office without a shred of proof. She went to our Account Manager (our boss on the security end) and to one of the building managers (the client whom we provide the security service for) anonymously. This coworker is known for "snitching" at work and has lied before to get other coworkers into trouble with our boss. She's been heavily favored by our boss, along with a small group of other coworkers, for years and this, along with the snitching also done by this group, has created a very toxic workplace environment. Emails were sent by building management to security heads at my company and ultimately HR and a decision was made to terminate my employment. Do I have a case here?