Learning Participles and a little Lysias

Here's an excerpted translation of the Lysias passage:

When Adrastus and Polyneices marched against Thebes and were defeated in battle, and the Cadmeians would not allow the burial of the corpses, the Athenians judged that those men paid the utmost penalty by dying, that the gods were being treated with impiety. Sending heralds first, they requested that the Thebans allow them to take up the corpses. When they could not obtain their request, they marched against the Cadmeians, although no previous quarrel existed with the Thebans. Rather, considering it right that those killed in the war obtain the customary rites, ... they fought and gained victory with justice as their ally, they displayed to all their bravery.

"with justice as their ally," ... I loved it when I came to that phrase,
"dikaion exontes symmachon," and understood what it meant, quite
accurately, in the context of the sentence.