Commutative magma implies all nuclei coincide

Statement
In a fact about::commutative magma, the fact about::left nucleus, fact about::middle nucleus and fact about::right nucleus all coincide, and are all equal to the nucleus of the magma. In other words, an element of the magma is left-associative if and only if it is middle-associative if and only if it is right-associative.

Related facts

 * Inverse property loop implies all nuclei coincide