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"If you think that you only deserve a certain amount and that's not correct, it's about changing that mindset and sticking up for yourself the way," Cooper explained to E! News, adding that he had not yet read Lawrence's essay "Why Do I Make Less Than My Co-Stars."
"So that's a great thing," he added.
Actress Sienna Miller, Cooper's co-star in "Burnt," told E! earlier that she had backed out of a play "because I was offered less than half of what the other man was offered and it was just the two of us."
In her essay on Lena Dunham's newsletter Lenny, Lawrence wrote that she discovered that she and "American Hustle" co-star Amy Adams were getting paid much less than their male co-stars Jeremy Renner, Christian Bale and Cooper. The actors' pay was released publicly after Sony Pictures Entertainment was hacked in 2014.
"I didn’t get mad at Sony," wrote Lawrence. "I got mad at myself. I failed as a negotiator because I gave up early. I didn’t want to keep fighting over millions of dollars that, frankly, due to two franchises, I don’t need."
The 25-year-old Oscar winner said that she didn’t want to come off as "difficult" or "spoiled" during salary negotiations.
"I would be lying if I didn’t say there was an element of wanting to be liked that influenced my decision to close the deal without a real fight," Lawrence wrote.
Cooper was still standing by his friend when he talked to "Entertainment Tonight."
"There's a double standard in the whole world, yeah, for sure. This is just one aspect," Cooper said. "Anytime there's a place where a voice can come out and be outspoken -- something Sienna did, or Jennifer -- that's great. ... I think it is making a difference."
Lawrence's essay drew reactions from other Hollywood stars, who voiced their support on social media.
O Jennifer Lawrence I love you so. X— Emma Watson (@EmWatson) October 13, 2015
"I’m over trying to find the “adorable” way to state my opinion".— Emma Watson (@EmWatson) October 13, 2015
Yessssssss! Get it girl xx https://t.co/L3w0nNnqGQ— Jessica Chastain (@jes_chastain) October 13, 2015
I love Jennifer Lawrence. http://t.co/x2jAbnUsmy— Elizabeth Banks (@ElizabethBanks) October 13, 2015