= Galvin theorem for bipartite list edge coloring
{c}
{title2=$\chi\prime_\ell(G)=\chi\prime(G)=\Delta(G)$}
A <bipartite graph> has equal <list-chromatic index>, <chromatic index> and <maximum degree of a graph> $\Delta$. Start with a proper $\Delta$-<edge coloring>. Orient its <line graph> toward smaller colors at one part and toward larger colors at the other. An edge of color $c$ has at most $(c-1)+(\Delta-c)=\Delta-1$ outgoing neighbours. Every induced orientation has a <digraph kernel> obtained from a <stable matching in a bipartite graph> with those preferences. Apply the <kernel list-coloring lemma>.
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