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.