Biconditional introduction: Difference between revisions

Revision as of 15:19, 21 February 2012

Revision as of 21:21, 22 February 2012

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{{Transformation rules}}

#REDIRECT [[If and only if]]

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".

Formally, biconditional introduction is the rule schema.

:<math> A \to B \, </math>

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

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

{{DEFAULTSORT:Biconditional Introduction}}

[[Category:Rules of inference]]

[[Category:Mathematical logic]]

[[Category:Propositional calculus]]

[[eo:Dukondiĉa enkonduko]]