Assume the conjunction and obtain a contradiction in each of the two cases supplied by the premise:
LineFormulaJustification
1Premise
2Assume locally
3Conjunction elimination rule, left, 2
4Conjunction elimination rule, right, 2
5Assume first case
6Negation elimination rule, 3 and 5
7Assume second case
8Negation elimination rule, 4 and 7
9Disjunction elimination rule, 1, 5–6 and 7–8
10Negation introduction rule, discharging 2–9
The two case assumptions disappear at line 9, while the conjunction assumption remains available until line 10. The proof uses only the primitive rules printed in the paper.

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