Biconditional introduction

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.

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

$A\to B\,$

${\underline {B\to A}}$

$A\leftrightarrow B$

See also

• Logical biconditional