Constant Function is Uniformly Continuous/Real Function

Theorem
Let $f_c: \R \to \R$ be the constant mapping:
 * $\exists c \in \R: \forall a \in \R: \map {f_c} a = c$

Then $f_c$ is uniformly continuous on $\R$.

Proof
Follows directly from:
 * Constant Function is Uniformly Continuous: Metric Space
 * Real Number Line is Metric Space.