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-[ A -> B |- ~ B -> ~ A ]
------------------------------- Implication strategy
-[ A -> B , ~ B |- ~ A ]
------------------------------- Negation rewrite
-[ A -> B , ~ B |- A -> _|_ ]
------------------------------- Implication strategy
-[ A , A -> B , ~ B |- _|_ ]
------------------------------- Modus ponens
-[ A , A -> B , B , ~ B |- _|_ ]
------------------------------- Forgetting
-[ B , ~ B |- _|_ ]
------------------------------- Ex falso quodlibet _|_