Tautological consequence

Concept in propositional logic

In propositional logic, tautological consequence is a strict form of logical consequence in which the tautologousness of a proposition is preserved from one line of a proof to the next. Not all logical consequences are tautological consequences. A proposition is said to be a tautological consequence of one or more other propositions in a proof with respect to some logical system if one is validly able to introduce the proposition onto a line of the proof within the rules of the system; and in all cases when each of are true, the proposition also is true.

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