When that document was signed in 1776, actually a few days before July 4, it made the abolition of slavery and women’s suffrage inevitable. By 1863, slavery would be a thing of the past, and by 1869, women would be legal and acknowledged voters.
(Many textbooks give the impression that woman began voting in 1920 in the United States. In fact, approximately 75% of women were voting before then.)
The debates and discussions of the 1850s show how the Declaration of Independence had made the end of slavery a historical inevitability. Lincoln’s drive toward abolition was fueled by the text of that document, as historian Mark Levin writes:
Many decades after America’s founding, Abraham Lincoln relied heavily on the Declaration of Independence and the principles embedded in it to provide the essential moral justifications for liberty, equality, and, of course, ending slavery - the natural and equal rights of the individual. Lincoln revered the Declaration and repeatedly quoted and referenced it in his speeches, debates, and writings before and after he became president.
Texts from the 1770s show that it was not merely an opinion or preference, among the Americans in general and among the representatives at the Continental Congress, but rather an explicit goal that slavery be ended. Lincoln was able to apply their words to achieve that objective.
He used it again and again as a cudgel against the proslavery forces and slavery accommodationists. For example, on August 17, 1858, in Lewistown, Illinois, Lincoln delivered a powerful speech during his campaign for the U.S. Senate against Stephen A. Douglas, in which he verbally brandished the Declaration in his condemnation of slavery.
Lincoln had dedicated himself, his political party, and his career to the abolition of slavery. Although his speeches remain admired for their brilliance, he used the words of others - the words of Thomas Jefferson, George Washington, Benjamin Franklin, Samuel Adams, James Otis, Thomas Paine, Patrick Henry, etc. - to free the slaves.
The Emancipation Proclamation of 1863 is an organic outgrowth of the Declaration of Independence. The end of slavery was contained, if latently, in the text of July 4, 1776.