It is very easy to prove. Note first that ~P is an abbreviation for P -> False. So we can rewrite this as (~ ~ P -> False) -> P -> False. This is tautologically

It is very easy to prove. Note first that ~P is an abbreviation for P -> False. So we can rewrite this as (~ ~ P -> False) -> P -> False. This is tautologically true by modes ponens if P -> ~ ~ P. But that is a well known fact.