CHEYENNE, Wyo. — Liz Cheney, daughter of former Vice President Dick Cheney, swept to victory in a crowded race for the Republican nomination for Wyoming’s lone seat in the U.S. House — a post once held by her father.

Her victory Tuesday in the Republican primary likely signals that she will win the seat in the general election this fall. Party registration favors the GOP over Democrats better than three-to-one in Wyoming, and no Democrat has held the seat since Dick Cheney’s predecessor in the 1970s.

In an interview with The Associated Press, Liz Cheney said Tuesday that she couldn’t be prouder of being Dick Cheney’s daughter. “Certainly we’ve been served well by many people in Washington, and it is very special to have been nominated to serve in the seat that my dad held,” she said.

Her victory also marks a comeback from her first shot at Wyoming politics in 2014, when she brashly challenged Sen. Mike Enzi, the state’s senior Republican.

Many prominent Wyoming Republicans accused Liz Cheney two years ago of being a “carpetbagger” and criticized her for challenging GOP incumbent Enzi when she had only recently moved to Wyoming from Virginia. She quickly dropped out of the race.

This time around, however, she and seven other Republicans were vying for an open House seat. Rep. Cynthia Lummis is not seeking re-election.

A former Fox News commentator and State Department official, Liz Cheney drew on her national contacts in funding her primary victory. She brought in more than $1.5 million through July, banking almost 10 times more money than her next three opponents combined.