The eldest daughter of Bruce Willis and Demi Moore talks to PEOPLE about her sister's recovery

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There’s nothing like that sisterly bond.

Rumer Willis, eldest daughter of Demi Moore and Bruce Willis, is beaming with pride over her younger sister Tallulah‘s recovery after seeking treatment for various issues.

“I’ve actually been so impressed and blown away by her strength and her openness and willingness,” Rumer, 26, told PEOPLE at Thursday’s Samsung Note Pad event in Beverly Hills to celebrate the launch of the Galaxy Note 4. “Not only to move past things but also to share herself with other people.”

Tallulah, 20, returned home at the beginning of September after six weeks in treatment. The fashion blogger opened up about her struggles with an eating disorder and body dysmorphia in a candid video interview.

Rumer says her younger sister is now doing “great. She’s doing really well!”

Rumer grew up in Idaho for most of her teenage years and attributes some of Tallulah’s difficulties to growing up under the spotlight in Los Angeles.

Of her siblings (Scout Willis is 23), Rumer says, “They kind of grew up more here, so in a way, it’s interesting because they ve had such a different experience than I had. They moved out to L.A. when they were younger, so they were kind of exposed to everything a lot more.”

A source told PEOPLE in August that Tallulah had been “adversely affected” by her parents’ 2000 divorce, and a former high school classmate said that Moore’s 2012 hospitalization also weighed heavily on her.

“When you grow up like we do, everyone has an opinion of you. Everyone wants to put you in a particular box,” says Rumer. “If you get photographed the wrong way or you’re at a party, it doesn’t matter if you’re drinking or not, you know, it’s whatever the perception is. So if you allow yourself to find your value in other people’s perceptions of you, then you will never be happy, whether it’s good or bad.”

Rumer, though, has had her younger sibling’s back from the beginning.

“The best thing you can do for anyone in your life that you know is struggling with anything is just to be supportive and not abandon them,” she says. “Because I think that’s the hardest thing, when you’re going through something and you feel alone and you feel like people don’t have your back.”

Reporting by CHRISTINA DUGAN

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