But the early contest could also catapult another woman into an unprecedented position of power. A sound defeat for Labour could oust leader Jeremy Corbyn and make one of the women in contention to replace him the party’s first-ever female head.

When asked about his post-election fate on Tuesday, Corbyn told Sky News, “We are campaigning to win this election, that’s the only question now.” In a longer statement, Corbyn said he “welcomed” the prime minister’s decision “to give the British people the chance to vote for a government that will put the interests of the majority first.” But already, a Labour MP signaled his opposition to Corbyn’s leadership ahead of the contest by saying he would not stand for reelection as a Labour candidate due to his disagreements with Corbyn.

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Corbyn has been at odds with some members of his own party since the Brexit referendum last June after giving what some saw as a half-hearted endorsement of the “Remain” campaign. He lost a no-confidence vote in late June following a mass exodus from his shadow cabinet, but he was reelected in September with 61.8% of the vote, a larger margin of victory than the prior year.

When Corbyn came under fire last summer, two names—Angela Eagle and Yvette Cooper—were floated as possible replacements, but neither of them formally challenged the incumbent.

British odds-maker Ladbrokes—which allows Brits to legally bet on political outcomes—calculated the odds of Cooper, the former shadow home secretary, succeeding Corbyn at 12-1 on Tuesday. The odds for Eagle, a veteran MP first elected in 1992, were much longer at 50-1. Both those women, however, had been leapfrogged by three other female MPs with shorter odds: Shadow Secretary of State for Business, Energy and Industrial Strategy Rebecca Long-Bailey, former Shadow Secretary of State for Energy and Climate Change Lisa Nandy, and Angela Rayner, who was appointed the shadow education secretary in July. Three male MPs—Clive Lewis, Keir Starmer, and Dan Jarvis—have the best odds of replacing Corbyn, according to the betting house.

A female leader would be a first for a Labour Party that espouses gender equality and relies on all-women shortlists to field candidates. Should a woman take the helm, she would join the ranks of female political party leaders that has grown of late. Leanne Wood leads Wales’ Plaid Cymru party, Arlene Foster heads the Democratic Unionists, the Scottish National Party is overseen by First Minister Nicola Sturgeon, and May, of course, is the Conservative leader.

Women have made big advances, relatively speaking, in the U.K.’s parliament since the trailblazing Margaret Thatcher became the country’s first female leader in 1979. Back then, Thatcher was one of only 19 women in parliament (a mere 3% of the total). By the time she was forced from office in 1991, women were still only 9% of all MPs. Today, the figure is at 30%, and still clearly on a rising trend (the U.S. Congress is 19% female, by comparison).

But there’s still a long way to go. Even at 30% representation, the U.K. is still only in 48th place globally—a ranking Women and Equalities Committee chair Maria Miller called “shockingly low” in January. “We must rise to the challenge of being a world leader on women’s parliamentary representation,” she said.