Let $f : \mathbb{R}^n \to \mathbb{R}^m$ be a D4363: Euclidean real function such that

(i)	$f_{\mathsf{even}} : \mathbb{R}^n \to \mathbb{R}^m$ is the D4692: Euclidean real function even part of $f$

Then $f_{\mathsf{even}}$ is an D3997: Even euclidean real function.