PHIL 250: Introduction to Symbolic Logic

tennant.9@osu.edu

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INTRODUCTION RULE FOR IMPLICATION (→I)

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_(i)_

A

:

:

B

______(i)

A→B

Explanation in words: In order to infer to a conclusion with a dominant occurrence of the conditional connective, one must deduce B---as indicated by the descending dots---with or without the help of the assumption A. By taking the indicated step of implication introduction (also known as conditional proof), one thereby discharges the assumption A, if one has used it in order to deduce B. This means that the conclusion A→B no longer depends on the assumption A. Instead, it depends only on whatever other assumptions might have been used, besides A, to deduce B.

Compare the corresponding elimination 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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