PHIL 250: Introduction to Symbolic Logic

tennant.9@osu.edu

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ELIMINATION RULE FOR DISJUNCTION (∨E)

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__(i)

__(i)

A

B

:

:

A∨B

C

C

__________________________________(i)

C

Explanation in words: In order to infer from a disjunctive premiss A∨B, to a desired conclusion C, one must prove C from the case assumption A, and prove C from the case assumption B. By taking the indicated step of disjunction elimination, one thereby rests the resulting conclusion C on the combination of: (1) the assumptions on which A∨B rests, (2) the assumptions of the first case proof (other than the case assumption A, which is discharged) and the assumptions of the second case proof (other than the case assumption B, which is also discharged).

Compare the corresponding introduction rule for ∨

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[¬I] [∧I] [∨I] [→I] [∀I] [∃I]
[¬E] [∧E] [∨E] [→E] [∀E] [∃E]
[EFQ]
[LEM] [Dil] [CR] [DNE]

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