Claudia Sheinbaum is projected to win Mexico's presidential election and become the nation's first female president in history.

"I will become the first woman president of Mexico," Sheinbaum said at a downtown Mexico City hotel shortly after electoral authorities announced a statistical sample showed she held an irreversible lead, according to The Associated Press. "I don't make it alone. We've all made it, with our heroines who gave us our homeland, with our mothers, our daughters and our granddaughters." 

The former Mexico City mayor said that her two competitors – Xóchitl Gálvez and Jorge Álvarez Máynez – had called her and conceded.  

The National Electoral Institute’s president said Sheinbaum had between 58.3% and 60.7% of the vote, according to a statistical sample. Opposition candidate Gálvez had between 26.6% and 28.6% of the vote, and Álvarez Máynez had between 9.9% and 10.8% of the vote. Sheinbaum's Morena Party was also projected to hold majorities in both chambers of Congress. 

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Sheinbaum, the AP reports, will also be the first Jewish leader of the overwhelmingly Catholic country. 

She will start her six-year term on Oct. 1. Mexico’s constitution does not allow re-election. 

The leftist has said she believes the government has a strong role to play in addressing economic inequality and providing a sturdy social safety net, much like her political mentor President Andrés Manuel López Obrador, who is also a member of the Morena Party. 

"Of course, I congratulate Claudia Sheinbaum with all my respect who ended up the winner by a wide margin," López Obrador said Monday. "She is going to be Mexico’s first (woman) president in 200 years." 

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The main opposition candidate, Gálvez, a tech entrepreneur and former senator, had promised to take a more aggressive approach toward organized crime. 

In her concession speech, she said, "I want to stress that my recognition (of Sheinbaum's victory) comes with a firm demand for results and solutions to the country's serious problems." 

Julio García, a Mexico City office worker, had told the AP he was voting for the opposition in Mexico City’s central San Rafael neighborhood.  

"They’ve robbed me twice at gunpoint. You have to change direction, change leadership," the 34-year-old was quoted as saying. "Continuing the same way, we're going to become Venezuela." 

The Associated Press contributed to this report.