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Both reductio ad absurdum and the rule of weakening have been challenged in this respect, but without much success. Double negation elimination is challenged, but for unrelated reasons. By removing it alone, while upholding the other two one may still be able to prove all negative propositions from a contradiction.
== I think there is a typo ==
Shouldn't the line that reads "Furthermore, inconsistency-robust proof by contradiction holds for entailment (A⇒(B∧¬B))⊢¬B." be "(A⇒(B∧¬B))⊢¬A"?
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