Under the premise, assuming either disjunct would introduce the forbidden logical disjunction. Discharging those two assumptions gives the two separate negations, which can then be conjoined.
Table 1.
Derivation of the two negated disjuncts
. | Line | Open assumptions | Formula | Justification |
|---|---|---|---|
| 1 | 1 | Premise | |
| 2 | 1, 2 | Temporary assumption | |
| 3 | 1, 2 | disjunction introduction L 2 | |
| 4 | 1, 2 | negation elimination rule 3, 1 | |
| 5 | 1 | negation introduction 2, 4 | |
| 6 | 1, 6 | Temporary assumption | |
| 7 | 1, 6 | disjunction introduction R 6 | |
| 8 | 1, 6 | negation elimination rule 7, 1 | |
| 9 | 1 | negation introduction 6, 8 | |
| 10 | 1 | conjunction introduction 5, 9 |
ThusThe redundant closing parenthesis printed after the conclusion on p. 8 does not alter the readable propositional formula.[ref]
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