Yes, predators eat other predators. But what you are describing is two “apex predators”, meaning there aren’t predators that generally attack and eat them.
But lions will eat crocodiles they catch out of the water, and crocodiles will eat lions that go for a drink.
Mountain lions eat foxes and coyotes, a good example of predators eating another predator.
Wolves only do well in a pack, but may get killed if by themselves.
But grizzly bears and mountain lions generally leave each other alone unless provoked or one is weakened.