Indeed, it is expressed correctly. The very first real Pride was in fact the Stonewall Inn Revolution in 1969. From the Wikipedia entry:

“The Stonewall riots, also known as the Stonewall uprising, Stonewall rebellion, or simply Stonewall, were a series of spontaneous, violent demonstrations against a police raid that took place in the early morning hours of June 28, 1969, at the Stonewall Inn, in the Greenwich Village neighborhood of New York City. Although the demonstrations were not the first instance in American history when people in the homosexual community fought back against a government-sponsored system that persecuted sexual minorities, they have become the defining event that marked the start of the gay rights movement in the United States and around the world.

…

“Following the Stonewall riots, sexual minorities in New York City faced gender, class, and generational obstacles to becoming a cohesive community. In the weeks and months after, they initiated politically active social organizations and launched publications that spoke openly about rights for gay people. The first anniversary of the riots was marked by peaceful demonstrations in several American cities that have since grown to become Gay Pride marches. The Stonewall National Monument was established at the site in 2016. Today, Gay Pride events are held annually throughout the world toward the end of June to mark the Stonewall riots.”

Wikipedia

Never forget our roots. You have to fight, and fight hard for your rights. They are never given to you freely.

[Photo: “Police force people back outside the Stonewall Inn as tensions escalate the morning of June 28, 1969. It illustrates the beginning of the riots. The value differences between riot participants and the police is reflected in this image, and directly led to the cause of the riots. It is the only published image of the riots during the first evening when they spontaneously began.” —Wikimedia Commons, Fair Use]