1-isomorphism is direct product-closed

Statement
Suppose $$I$$ is an indexing set and $$G_i, H_i$$ are fact about::1-isomorphic groups for each $$i \in I$$. Then, the fact about::external direct product of the $$G_i$$s is 1-isomorphic to the external direct product of the $$H_i$$s.

Related facts

 * Order statistics-equivalence is finite-direct product-closed
 * Direct product is cancellative for order statistics-equivalence