= Solution
Use <disjunction introduction>, <negation introduction> and <conjunction introduction> in the following <natural deduction> proof. Indentation marks the assumptions discharged at their closing lines.
``
1. ¬(φ ∨ ψ) premise
2. φ assumption [i]
3. φ ∨ ψ ∨I-left, 2
4. ⊥ ¬E, 1, 3
5. ¬φ ¬I, 2–4, discharging [i]
6. ψ assumption [j]
7. φ ∨ ψ ∨I-right, 6
8. ⊥ ¬E, 1, 7
9. ¬ψ ¬I, 6–8, discharging [j]
10. ¬φ ∧ ¬ψ ∧I, 5, 9
``
The two separate temporary assumptions establish the two required negations; neither is retained in the conclusion.
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