Barbara and Not Bocardo

I keep bumping into this in the context of a 40s/50s Film Noir or Hitchcockian flick, where the detective gets a sudden flash of insight and says, “Then it was Barbara and not Bocardo who dunnit!”

Searching, I find that Barbara and Bocardo are nicknames given to specific Aristotelian syllogisms! (A “Bocardo” is of the form “Not all A are B. All A are C. Thus, not all C are B.”)

Which is the cart, and which the horse? i.e., which came first, the movie reference or the logicians’ nicknames? And…what the heck movie is it, anyway?

Trinopus