Right Operation is Associative

Theorem
The right operation is associative:


 * $$\forall x, y, z: \left({x \rightarrow y}\right) \rightarrow z = x \rightarrow \left({y \rightarrow z}\right)$$

Proof
By the definition of the right operation:

$$ $$

$$ $$

Hence the result.

Also see

 * Left Operation is Associative