---
tag: R698F4HZ51
kind: concept
name: Biconditional introduction
sources:
  - wikipedia: en:4286@r1168208951
    locator: Biconditional introduction
    note: adopted
    mention: wikipedia://en/4286
    sections: [Summary]
same_as:
  wikidata: Q4903714
  wikipedia: Biconditional introduction
inventory: [CD25W4D94A]
---

## Summary

In propositional logic, **biconditional introduction** is a valid rule of inference. It allows for one to infer a biconditional from two [[conditional statements|0NMG7W7Q11]]. The rule makes it possible to introduce a biconditional statement into a logical proof. If $P \to Q$ is true, and if $Q \to P$ is true, then one may infer that $P \leftrightarrow Q$ 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|09A3N7ZN5G]] of biconditional elimination. The rule can be stated formally as: