The old body/mind is seen to be just one of billions of body/minds. It holds no more, or less significance than any of the others.
In reality they are all you. All creatures are you. All trees and plants are you. All rocks and rivers and mountains and stars and planets are you.
When this is realised, when this is known, when this becomes the one experience, then awakening is attained. One is consciousness itself and consciousness is One.