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René Descartes' Truth Tree: Deriving the Cogito (from Self Evident Premises)

  ¬E → ¬D   If I do not exist, then I cannot do anything.
  P → D   If I perceive thoughts, then I am doing something.
  P   I perceive thoughts.
T → E   If I think, therefore I am (Cogito, ergo sum).

... which we can make into a truth tree.

¬(T → E) Negation of Conclusion.
 
T ∧ ¬E Logical Transformation
 
T  
"AND" Statement
¬E  
 
¬E → ¬D Premise 1
↙      ↘  
E            ¬D "If-Then" Statement
X               ↓  
                   P → D Premise 2
                 ↙        ↘  
               ¬P                D "If-Then" Statement
                 ↓                 X  
                P                     
                X                     

All Branches Are Closed!
The Argument is Valid!