In propositional logic, biconditional introduction is a valid rule of inference. It allows for one to infer a biconditional from two conditional statements. The rule makes it possible to introduce a biconditional statement into a logical proof. If is true, and then one may infer that is true. For example, from the statements "if I'm breathing, then I'm alive" and "if I'm alive, then I'm breathing", it can be inferred that "I'm breathing if and only if I'm alive". Biconditional introduction is the converse of biconditional elimination. The rule can be stated formally as:
where the rule is that wherever instances of "" and "" appear on lines of a proof, "" can validly be placed on a subsequent line.
Other articles related to "biconditional introduction":
... Biconditional introduction allows you to infer that, if B follows from A, and A follows from B, then A if and only if B ...
... The biconditional introduction rule may be written in sequent notation where is a metalogical symbol meaning that is a syntactic consequence when and are both ...
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