California colleges will be required to adopt rape-prevention policies that include a so-called “affirmative consent” standard before sexual activity under a new law signed by Gov. Jerry Brown (D) over the weekend.

The standard, also dubbed “yes means yes,” will require people to receive what the bill defines as “affirmative, conscious and voluntary agreement” from their partners before engaging in sexual activity. The legislation, sponsored by incoming state Senate President Kevin de Leon (D), aims to cut the prevalence of sexual assault on college campuses.

The law also says anyone asleep, unconscious or intoxicated is unable to give consent.

Sexual assault survivors groups delivered petitions with thousands of signatures to Brown’s office  Sept. 16. The presidents of the University of California, California State University and California Community College systems all backed the bill, too.

“The State of California will not allow schools to sweep rape cases under the rug. We’ve shifted the conversation regarding sexual assault to one of prevention, justice, and healing,” de Leon said in a statement late Sunday.

The new law applies to all colleges and universities that accept any funding from the state. The policies those colleges must adopt will also be required to include victim-centered sexual assault response policies and prevention programs.

The bill was one of 48 Brown signed into law  Sunday, two days before a Sept. 30 deadline requiring him to act on legislation passed this year.