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[ |- (A -> B) v (B -> A) ]
------------------------------ Reductio ad absurdum
[ ~ ((A -> B) v (B -> A)) |- _|_ ]
------------------------------ de Morgan 1
[ ~ (A -> B) & ~ (B -> A) |- _|_ ]
------------------------------ Conjunction split
[ ~ (A -> B), ~ (B -> A) |- _|_ ]
------------------------------ Implication negation
[ A, ~ (B -> A) |- _|_ ]
------------------------------ Implication negation
[ A, ~ A |- _|_ ]
------------------------------ Ex falso quodlibet _|_
Ø
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