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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 _|_