# Exponential is Strictly Increasing/Proof 1

## Theorem

The function $\map f x = \exp x$ is strictly increasing.

## Proof

By definition, the exponential function is the inverse of the natural logarithm function.

From Logarithm is Strictly Increasing, $\ln x$ is strictly increasing.

The result follows from Inverse of Strictly Monotone Function.

$\blacksquare$