The original scan repeats the premise and conclusion of part (i) exactly; it is not a missing or unreadable alternative exercise.[ref] Here is a second formal ordering of the same argument. First introduce the fresh existential witness, derive the desired negation inside its scope, and then eliminate the witness:
Table 1.
Close the negation subproof before eliminating the witness
.
LineOpen assumptionsFormulaJustification
11Premise
21, 2Temporary assumption
31, 2, 3Temporary assumption
41, 2, 3universal elimination 3; term
51, 2, 3negation elimination rule 2, 4
61, 2negation introduction 3, 5
71existential elimination 1, 2, 6; fresh
Thus, again,
(1)
At the last existential elimination, occurs in neither the exported conclusion nor the remaining premise. The eigenvariable condition is therefore satisfied. This proof retains a different nesting of the subproofs from part (i).

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