left and right distributivity are both equivalent to distributivity.

Existential axioms

Some common axioms contain an existential clause. In general, such a clause can be avoided by introducing further operations, and replacing the existential clause by an identity involving the new operation. More precisely, let us consider an axiom of the form "for all there is such that $f(X,y)=g(X,y)$ ", where is a -tuple of variables. Choosing a specific

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