It was one of the tea party’s few highlights in March’s congressional primaries. But laying claim to former GOP House speaker John Boehner’s old seat is a big one, both for the bragging rights and the momentum it gives House conservatives in their ongoing fight to purify their party ideologically.

Warren Davidson, a businessman and former Army Ranger, won a 15-way Republican primary in March in the special election for Ohio’s 8th Congressional District. The tea party candidate rather easily bested more moderate candidates, including two state lawmakers, in a campaign that quickly became ground zero for the party’s ongoing identity struggle in the House that Boehner used to run.

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On Tuesday, Davidson easily won the special election in the deep-red district, which will allow him to serve out 2016 in Boehner’s seat.

Let’s step back and assess why this matters. Sure, adding one lawmaker to the ranks of the hard-line House conservatives who have made life difficult for their moderate, pro-business Republican colleagues won’t single-handedly change the outcomes of most intra-party dramas. Davidson also won in large part thanks to a crowded primary; he took less than one-third of the vote.

(His general election victory was much smoother. On Tuesday, the Associated Press called the race after Davidson won 75 percent of the vote of 48 precincts reporting.)

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But you can imagine how good it feels for the conservatives to get to say they took the former speaker’s seat, especially after spending the past few years directly challenging Boehner and, eventually, forcing him out. Congressional conservatives and their outside backers can now reasonably claim they won two battles against Boehner: They played a role in forcing his retirement last fall, and then they won the seat he vacated this spring.

Boehner’s successor, House Speaker Paul D. Ryan (R-Wis.), is also trying to work with or around an estimated 30 to 40 hard-line conservatives who are expressing the same intransigence over budget and social issues that Boehner struggled with.

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Davidson’s win could give those lawmakers more reason to dig their heels in as things escalate. They can make their case to Republican leaders that, sure, putting their foot down on a proposed budget that increases spending might hinder Republicans’ goal of passing a budget on time. But what they’re doing is really in the interest of a growing number of Republican voters. Look no further than this highly symbolic seat they just won.

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The head of the conservative Club for Growth predicted to Politico before the primary, the first big open House primary this year, that Boehner’s seat would be “a bellwether for what Republican primary voters are looking for now.”

Speaking of outside groups, several of them sensed the momentum that could come from a win and tried to factor heavily in this race. The Club for Growth spent a eyebrow-raising $1 million on TV ads to prop up Davidson and attack his rivals. And a new nonprofit aimed at supporting moderate conservatives, Right Way Initiative, spent $450,00 backing state Rep. Tim Derickson, who came in second. Boehner did not endorse anyone, though many of his allies were backing more establishment-oriented candidates.

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Taking you back to March’s primary, we’ll point out again that the size of the primary field probably didn’t help any candidates’ chances by splitting the ticket. And the Cincinnati Enquirer talked to several voters on election night who couldn’t remember who they voted for in the huge field.