Constant Operation is Associative

Theorem
Let $S$ be a set.

Let $x \left[{c}\right] y = c$ be a constant operation on $S$.

Then $\left[{c}\right]$ is an associative operation:

$\forall x, y, z \in S: \left({x \left[{c}\right] y}\right) \left[{c}\right] z = x \left[{c}\right] \left({y \left[{c}\right] z}\right)$

Proof
Hence the result.