Biconditional introduction: Difference between revisions

Revision as of 20:52, 18 August 2011

Revision as of 09:44, 18 February 2012

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{{Transformation rules}}

{{Rules of inference}}

In [[mathematical logic]], '''biconditional introduction''' is the [[rule of inference]] that, if B follows from A, and A follows from B, then A [[if and only if]] B.

In [[propositional calculus|propositional logic]], '''biconditional introduction''' is a [[validity|valid]] [[rule of inference]]. It makes it possible to introduce a [[logical biconditional|biconditional]] into a [[formal proof|logical proof]]. If the statement that ''A implies B'' and also the statement that ''B implies A'' both appear in a proof, then one may introduce the statement ''A [[if and only if]] B'' or formally, ''(A ↔ B)''.

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".

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:<math> \underline{B \to A} </math>

:<math> A \leftrightarrow B </math>

==See also==

*[[Logical biconditional]]

{{DEFAULTSORT:Biconditional Introduction}}