The reductio ad absurdum rule discharges an assumption from a derivation of contradiction and concludes . It is derivable using negation introduction followed by double-negation elimination:
(1)
Conversely, if RAA is supplied, double-negation elimination follows from this natural deduction derivation:
1. ¬¬φ                  premise
2.   ¬φ                 assumption [i]
3.   ⊥                  ¬E, 1, 2
4. φ                    RAA, 2–3, discharging [i]
Thus replacing double-negation elimination by RAA leaves these classical deductions available. RAA is not being assumed as an intuitionistic rule.

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