Let $M = (X, d)$ be a D1107: Metric space such that

(i)	$X \neq \emptyset$
(ii)	$M$ is a D194: Complete metric space
(iii)	$f : X \to X$ is a D49: Proper contraction on $M$

Then \begin{equation} \# \{ x \in X : f(x) = x \} = 1 \end{equation}