The argument is structured as a reduction ad absurdum. This means that he starts with an assumption that will lead to a contradiction later, and thus disproves the original assumption.
Descartes starts with the assumption: "I am is a deception." This means that even "I exist" is something that might be a deception by an evil demon.
A deception, however, includes that somebody must be deceived. Even an evil demon is not deceiving nobody. If we take this into account it means that the evil demon deceives somebody of being himself.
This, however, is a contradiction, since the one who is deceived cannot be deceived of being the one who is deceived. If this is, therefore, a contradiction the original assumption must be false and its opposite must be true.
The opposite is: I am not a deception.
From this follows that even the strongest doubt cannot destroy the belief that I am, and thus I am, is an indubitable assumption. This "I am" is in the mode of thinking, since it tries to deny itself by virtue of thoughts. From this follows: I think, I exist.
6 Minutes, 1 minute revised
Proof of my existence (Reductio ad absurdum)
1. Assumption: The proposition “I am“ is a deception
2. Nevertheless, a deception means that somebody is deceived
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*Therefore: I am deceived of being deceived
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This is a contradiction, since I am the one who is deceived, so I am actually not deceived, I exist
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Final Conclusion: There must be something that is deceived that is me… this is a claim for existence
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