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The White House affirmed on Thursday President Trump has started the process for nominating a successor to U.S. Associate Justice Anthony Kennedy, but won’t say if that choice will uphold his legacy on LGBT rights.

White House Deputy Press Secretary Lindsay Walters dodged a question Thursday on whether LGBT rights would inform Trump’s pick from a reporter during a press gaggle on Air Force One en route to Wisconsin for a Trump rally.

Asked about the timing for Trump would make his announcement for his pick to replace in the aftermath of his announced retirement this week, Walters vaguely said “the process has already begun.”

“The president’s nominee to replace Justice Kennedy will have a tremendous intellect, judicial temperament and impeccable qualifications,” Walters added. “He or she, above all, will have a duty to uphold the law and the Constitution. And this is a process that the President has begun.”

Pressed for clarification on this process, Walters referenced Trump’s remarks in which he said he’d make his pick from a previously established list of 25 choices, but offered no further details.

“As the president said yesterday, he is going through the process of finding a nominee,” Walters said. “He will pick one off of the list that you all have previously seen. This is something that the president takes very seriously, and we will move through that process.”

When asked if Trump’s pick would carry the Kennedy legacy of upholding LGBT rights at the Supreme Court, Walters repeated her first response.

“As I said, the president’s nominee to replace Justice Kennedy will have a tremendous intellect, judicial temperament, and impeccable qualifications,” Walters said. “He or she, above all, will have a duty to uphold the law and the Constitution.”

During his 30 years on the Supreme Court, Kennedy was the author of milestone gay rights decision. The 1996 decision in Romer v. Evans held state laws barring municipalities from enacting LGBT non-discrimination ordinances are unconstitutional. Kennedy also wrote the 2003 decision in Lawrence v. Texas, which struck down state laws criminalizing same-sex relations.

Kennedy wrote decisions enacting marriage equality throughout the country, first with the 2013 decision in Windsor v. United States against the Defense of Marriage Act, a federal law barring federal recognition of same-sex marriage, then with the 2015 decision in Obergefell v. Hodges, which struck down state bans on same-sex marriage and guaranteed marriage equality through the country.