Courtesy of
Merriam-Webster "a: to have real being whether material or spiritual <did unicorns exist> <the largest galaxy known to exist> b : to have being in a specified place or with respect to understood limitations or conditions <strange ideas existed in his mind>
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In this context I do not need to prove my "existence". I percieve my own thoughts and actions in my mind. If nothing else I exist in my mind which I realize could simply become a mirror within a mirror but at that point the discussion is completely pointless. Even if I'm only shadows on the cave wall I still exist as a shadow, a representation of something else, either an idea or a physical reality. Either way, I exist, other exist in the same way. I can interact and respond to them if only in my mind. I will continue to do so until my physical being or shadow is destroyed.
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"Always learn the rules so that you can break them properly." Dalai Lama
My Karma just ran over your Dogma.