Johnny DeppandAmber Heardare now both in the process of appealing the verdicts in their Virginia defamation case.

Reps for Heard did not immediately respond to PEOPLE’s request for comment.

Last week, Judge Penney Azcaratedenied Heard’s request for a mistrial. In a statement Thursday about moving forward with the appeal — which will require Heard to post a bond of the full damages amount she owes — a spokesperson for Heard said they “believe the court made errors that prevented a just and fair verdict consistent with the First Amendment.”

“We are therefore appealing the verdict,” they added. “While we realize today’s filing will ignite the Twitter bonfires, there are steps we need to take to ensure both fairness and justice.”

JIM LO SCALZO / POOL/POOL/AFP via Getty Images

Johnny Depp arrives at the Fairfax County Circuit Courthouse in Fairfax

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When theyspoke out about the outcomeof their contentious six-week trial on June 1, Depp said he felt like the jury “gave me my life back,” while Heard said the verdict would be a “setback” for women who speak out.

Said Depp at the time, “My decision to pursue this case, knowing very well the height of the legal hurdles that I would be facing and the inevitable, worldwide spectacle into my life, was only made after considerable thought. From the very beginning, the goal of bringing this case was to reveal the truth, regardless of the outcome. Speaking the truth was something that I owed to my children and to all those who have remained steadfast in their support of me. I feel at peace knowing I have finally accomplished that.”

“The best is yet to come and a new chapter has finally begun,” he added.

Heard, meanwhile said, “I’m heartbroken that the mountain of evidence still was not enough to stand up to the disproportionate power, influence and sway of my ex-husband.”

STEVE HELBER/AFP/Getty

Actress Amber Heard, right, stands next to her attorney Elaine Bredehoft,

“I believe Johnny’s attorneys succeeded in getting the jury to overlook the key issue of Freedom of Speech and ignore evidence that was so conclusive that we won in the U.K.,” she added. “I’m sad I lost this case. But I am sadder still that I seem to have lost a right I thought I had as an American — to speak freely and openly.”

When she did a subsequent sit-down interview with NBC News’Savannah Guthrie, Heard said she holds no ill will for Depp and admittedshe understands how the jury reached its decision.

“How could they not come to that conclusion?” she said. “They had sat in those seats and heard over three weeks of nonstop relentless testimony from paid employees and, towards the end of the trial, randos, as I say. … I don’t blame them. I actually understand. He’s a beloved character and people feel they know him. He’s a fantastic actor.”

Separately, Heard is in alegal battle with her insurance providerover who is liable for paying her court fees, and Deppreached a pre-trial settlementwith a crew member from one of his movies who accused him of assault, which he denied.

source: people.com