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olligobber/Proof By Contradiction.txt

Created December 29, 2017 06:36
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A proof of "Proof by Contradiction" using propositional calculus as presented by Douglas R. Hofstader in "An Eternal Golden Braid"
Raw
Proof By Contradiction.txt
[
(P->(Q&~Q)) Premise
[
P Premise
(P->(Q&~Q)) Carry-Over
(Q&~Q) Detachment
Q Separation
~Q Separation
[
P Premise
Q Carry-Over
]
(P->Q) Fantasy
(~Q->~P) Contrapositive
~P Detachment
]
(P->~P) Fantasy
(~~P->~P) Double-Tilde
(~P|~P) Switcheroo
~~(~P|~P) Double-Tilde
~(~~P&~~P) De Morgan's
~(P&~~P) Double-Tilde
~(P&P) Double-Tilde
[
P Premise
(P&P) Joining
]
(P->(P&P)) Fantasy
(~(P&P)->~P) Contrapositive
~P Detachment
]
((P->(Q&~Q))->~P) Fantasy
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