Ambivalence is direct product-closed

Statement with symbols
Suppose $$I$$ is an indexing set and $$G_i, i \in I$$, is a collection of ambivalent groups. Let $$G$$ be the external direct product of the $$G_i$$s. Then, $$G$$ is also an ambivalent group.

Related facts

 * Every element is automorphic to its inverse is direct product-closed
 * Conjugacy-closed subgroup of ambivalent group is ambivalent