Derivative of Logarithm at One/Proof 3

Theorem
Let $\ln x$ be the natural logarithm of $x$ for real $x$ where $x > 0$.

Then:
 * $\displaystyle \lim_{x \mathop \to 0} \frac {\ln \left({1 + x}\right)} x = 1$

Proof
Note that this proof does not presuppose Derivative of Natural Logarithm Function.