Exponential Function is Continuous/Real Numbers/Proof 3

Theorem
The real exponential function is continuous.

That is:


 * $\forall x_0 \in \R: \displaystyle \lim_{x \to x_0} \ \exp x = \exp x_0$

Proof
This proof depends on the differential equation definition of the exponential function.

The result follows from Differentiable Function is Continuous.