Before "Looking Glass" in season 3 of DS9 was "Crossover" in season 2 where the Intendant confirms this directly to Kira:
INTENDANT: You didn't seem to recognise the Alliance.
KIRA: No.
INTENDANT: Perhaps you'd recognise the name Kirk.
KIRA: I'm sorry, I don't.
INTENDANT: Interesting. On my side, Kirk is one the most famous names in our history. Almost a century ago, a Terran starship Captain named James Kirk accidentally exchanged places with his counterpart from your side due to a transporter accident. Our Terrans were barbarians then, but their Empire was strong. While your Kirk was on this side, he met a Vulcan named Spock and somehow had a profound influence on him. Afterwards, Spock rose to Commander in Chief of the Empire by preaching reforms, disarmament, peace. It was quite a remarkable turnabout for his people. Unfortunately for them, when Spock had completed all these reforms, his empire was no longer in any position to defend itself against us.
KIRA: Us?
INTENDANT: The Alliance. The historic coming together of the Klingons and the Cardassians.
