That's not quite how I understand it. A core belief is one of the beliefs we form in early childhood about how the world and other people function in relation to ourselves. Because they are created so nm young and during a time when our grasp if language and logic are poor,; they are resistant to reason, logic, evidence and change. My understanding is core beliefs. Cover only a certain range of ideas. I am lovable/unlovable, I am accepted or there is something wrong with me and I am not like other people. I am capable of helping myself or helplesss. I deserve the same things as other people or I don't. Every one will leave me or people generally stay and care. The world is inherently good or inherently dangerous. I will be taken care of when needed or it is always my job to. Take care of others.

According to the reading I've done for example I am a vegetarian but my moral objection. To eating neat is NOT a core belief. They are very black and white and resistant to all contrary evidence, where as if someone proved to.me satisfactorily that my understanding of the experience of food animals is incorrect, I'd be open to changing my mind. With core beliefs since they are part of a pre logic view of the world, ; they are not responsive to evidence and we actually censor input to support them..

So it isn't just any strongly held belief. And usually negative core beliefs have significant negative effects on happiness and social functioning.