Absolutely Continuous Real Function is Continuous

Theorem
Let $I \subseteq \R$ be a real interval.

Let $f : I \to \R$ be an absolutely continuous function.

Then $f$ is continuous.

Proof
From Absolutely Continuous Function is Uniformly Continuous:


 * $f$ is uniformly continuous.

Therefore, from Uniformly Continuous Function is Continuous:


 * $f$ is continuous.