Who was the first woman to run for president?

In the year that Anthony cast her vote in the 1872 presidential election, Woodhull became the first woman put forward as a presidential candidate, nominated by the Equal Rights Party (with ex-slave Frederick Douglass running for Vice-President; Douglass never acknowledged this nomination, and it is possible that he saw it as an attempt to get "the colored vote" — black suffrage having been granted in the Fifteenth Amendment to the United States Constitution in 1870).