The triadjoint of an orthosymmetric bimorphism

summary:Let $A$ and $B$ be two Archimedean vector lattices and let $( A^{\prime }) _n'$ and $( B') _n'$ be their order continuous order biduals. If $\Psi \colon A\times A\rightarrow B$ is a positive orthosymmetric bimorphism, then the triadjoint $\Psi ^{\ast \ast \ast }\colon ( A') _n'\times ( A') _n'\rightarrow ( B') _n'$ of $\Psi $ is inevitably orthosymmetric. This leads to a new and short proof of the commutativity of almost $f$-algebras