Function in Differentiability Class 1 is also in Continuity Class

Theorem
Let $f$ be a real function.

Let $f$ be an element of differentiability class $C^1$.

Then $f$ is also an element of the class $C$ of continuous real functions.

Proof
By definition of $C^1$, $f \in C^1$ $f$ is differentiable.

By definition of $C$, $f \in C$ $f$ is continuous.

The result follows from Differentiable Function is Continuous.