Read the excerpt from "Woman's Rights to the Suffrage."

It was we, the people; not we, the white male citizens; nor yet we, the male citizens; but we, the whole people, who formed the Union. And we formed it, not to give the blessings of liberty, but to secure them; not to the half of ourselves and the half of our [descendants], but to the whole people – women as well as men. And it is a downright mockery to talk to women of their enjoyment of the blessings of liberty while they are denied the use of the only means of securing them provided by this democratic-republican government – the ballot.

Which fact supports Anthony's opinion that all adults should have the right to vote?

we, the whole people, who formed the Union.
they are denied the use of the only means of securing them . . .
And it is a downright mockery to talk to women . . .
not to give the blessings of liberty . . .

The fact that supports Anthony's opinion that all adults should have the right to vote is "we, the whole people, who formed the Union." This suggests that the formation of the Union included all people, not just a specific group, and therefore all people should have the right to vote.