 In normalizing an entire derivation, we can start by attacking the most deeply embedded classicizing detours (those in whose (original) indirect proof subproofs no further classicizing detours occur) and working outward. Combining this with applications of the earlier reductions, it is not hard to see that the entire derivation can be converted into one in normal form. Normal derivations in classical logic have only the weak (but still useful!) subformula property mentioned in  §5.3  in connection with Nelson’s variant of intuitionistic logic.