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a rule of inference in its own right. Conversely no rule of inference that has its own name gives rise to a logical equivalence. You will not find any reputable source that refers to this particular logical equivalence as a rule of inference. Furthermore material implication is neither a logical equivalence nor a rule of inference, it is an operation and it is simply wrong to call it anything else.
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On the contrary what you're referring to is a logical equivalence. Every logical equivalence vacuously gives rise to a derived rule of inference in which either side of the equivalence can be substituted for the other. Because it is vacuous one never dignifies any particular logical equivalence as
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For what it's worth, I have found it is possible to derive (in 25 lines) this "definition" using only the following rules of inference for natural deduction:
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a rule of inference, although (I believe) rarely under the name "material implication". —
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is correct. This article is completely broken. For correct usage see
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