Everything in the universe comes into being from other conditions. When certain conditions come together, phenomena are manifested, and when those conditions are absent, the manifested phenomena ceases to exist.
We are no different. When certain conditions come together, specifically a physical form, sensations, thought, a mental schema, and consciousness, our sense of an ego-self arises. When any one of these conditions is absent, the ego-self is gone.
There's an easy way to test this hypothesis. Find a comfortable place and sit there in an upright and alert posture. Breathe naturally, and perhaps watch your breath rise and fall for a few minutes. Try to ignore the thoughts that arise in your head, but don't try to suppress them either. Just let them go. Eventually, you might find yourself entering into a state not of "not thinking," but of "non-thinking," the distinction being that thinking hasn't stopped but attention to thought has. Of course, as soon as you recognize and identify this state, you're engaged in your thought again and have to start over. But once the thought is gone, the mental constructs of thought fall away, including the concept of an "I." To put it another way, when there is no more thinking, there is no thinker.
There's nothing at all mystical to this. Try it.
An interesting conclusion that comes from this experiment is in the recognition that the self is not a permanent and abiding thing, but comes and goes according to conditions. Bodies are born and bodies die, but there ultimately is no "self" that can be found that dies. This does not mean that we don't mourn the loss of people that we've known and loved, or want to cling to life while we are still alive, but it does reassure us that, in the end (literally) there is no real loss of anything.