---
tag: XDABNSBY2X
kind: concept
name: Biconditional elimination
sources:
  - wikipedia: en:4287@r1201988021
    locator: Biconditional elimination
    note: adopted
    mention: wikipedia://en/4287
    sections: [Summary]
same_as:
  wikidata: Q4903712
  wikipedia: Biconditional elimination
inventory: [T3AFEXWZDT]
---

## Summary

**Biconditional elimination** is the name of two valid rules of inference of propositional logic. It allows for one to infer a [[conditional|0NMG7W7Q11]] from a biconditional. If $P \leftrightarrow Q$ is true, then one may infer that $P \to Q$ is true, and also that $Q \to P$ is true. For example, if it's true that I'm breathing if and only if I'm alive, then it's true that if I'm breathing, I'm alive; likewise, it's true that if I'm alive, I'm breathing. The rules can be stated formally as: