Constant Function is 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 continuous on $\R$.

Proof
Follows directly from:
 * Constant Real Function is Uniformly Continuous
 * Uniformly Continuous Real Function is Continuous.