Let $f\_{=}$ be a function from $\mathbb{R}^{2}$ be defined as follows:
(1) if $x = y$ then $f\_{=}(x,y) = 1$; 
(2) $f\_{x,y} = 0$ otherwise.

I would like to have a proof for / a reference to a textbook proof of the following theorem (if it indeed is a theorem):

$f\_{=}$ is uncomputable even if one restricts the domain of $f\_{=}$ to a proper subset of $\mathbb{R}^{2}$, viz. the set of the computable real numbers

Thanks!