---
title: "If and only if mathematical notation"
description: "If and only if is a recurring research-paper notation family. States that each proposition implies the other, making both directions part of the claim."
canonical_url: "https://fanout.sh/labs/math-decoder/symbol/if-and-only-if"
md_url: "https://fanout.sh/labs/math-decoder/symbol/if-and-only-if.md"
last_updated: "2026-08-09"
access: "public"
---

# If and only if mathematical notation

If and only if is a recurring research-paper notation family. States that each proposition implies the other, making both directions part of the claim.

## Public overview

If and only if: States that each proposition implies the other, making both directions part of the claim. Example: Each statement is true exactly when the other is true.

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