The result of part (ii), with replaced by , first yields . To show every use of the derived rule explicitly, one can instead write:
1. ¬∃x ¬R(x)            premise
2.   ¬R(a)              assumption [i], a fresh
3.   ∃x ¬R(x)           ∃I, 2
4.   ⊥                  ¬E, 1, 3
5. ¬¬R(a)               ¬I, 2–4, discharging [i]
6. R(a)                 ¬¬E, 5
7. ∀y R(y)              ∀I, 6
The classical step is double-negation elimination at line 6. Freshness at line 7 holds after discharging the temporary assumption.

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