Bigraphs/digraphs of Ferrers dimension 2 and asteroidal triple of edges

Three mutually separable edges of a graph form an asteroidal triple of edges (ATE), if for any two of them, there is a path from the vertex set of one to the vertex set of another that avoids the neighbours of the third edge. In this note, it is shown that a bigraph of Ferrers dimension at most 2 is bichordal and ATE-free, but the converse is not true.