Are CW complexes absolute neighbourhood extensors?
A topological space $K$ is an absolute neighbourhood extensor (ANE) if for every space $X$, closed subset $A\subseteq X$, and continuous map $f:A\rightarrow K$, there is an open neighbourhood $U\subseteq X$ of $A$ and an extension $\tilde{f}:U\rightarrow K$ of $f$.
If one restricts the spaces $X$ in the above defintion to normal Hausdorff spaces, are CW complexes examples of ANE's?
I ask because I frequently see the kind of neighbourhood extension property described above used in proofs regarding the cohomological dimension of spaces.