Republican candidates who support former president Donald Trump' <a href="https://www.thenationalnews.com/world/us-news/2022/06/13/january-6-conspiracy-theories-and-debunked-claims/" target="_blank">2020 election falsehoods</a> emerged victorious in many US primaries for the midterm elections in November. Tuesday night's results also dealt a blow to Republicans who voted to impeach Mr Trump after the <a href="https://www.thenationalnews.com/world/us-news/2022/07/12/january-6-committee-probes-trumps-use-of-right-wing-extremists-to-fight-election/" target="_blank">January 6, 2021 attack</a> on the Capitol. Peter Meijer, one of 10 members of his party to vote in favour of impeachment, lost his Michigan primary to far-right challenger John Gibbs. Mr Gibbs, backed by the former president, was the beneficiary of Democratic advertising aimed at elevating more vulnerable Republican candidates in swing districts. Mr Meijer criticised the strategy the day before the vote in an <a href="https://www.commonsense.news/p/why-the-democrats-are-funding-my" target="_blank">online essay</a>. “As the January 6 Select Committee continues to warn about the ongoing threat to democracy, their own party dues are paying to help elect the same villains they rail against,” he wrote. Tudor Dixon, a conservator commentator who supports Mr Trump's false fraud claims, won the Republican nomination for Michigan governor. Ms Dixon, who received Mr Trump's endorsement last week, will face Democratic Governor Gretchen Whitmer in one of the midterm elections' highest-profile races. Another Republican who voted to impeach Trump, Jamie Herrera Beutler of Washington, also faced a Trump-endorsed primary challenger. The results of that race were not expected to be known until later on Wednesday or Thursday. Election officials in Arizona were still counting votes to determine the results of statewide races, but one notable result was the defeat of state <a href="https://www.thenationalnews.com/world/us-news/2022/06/21/january-6-hearings-promise-new-drama-as-investigation-continues-to-unfold/" target="_blank">House speaker Rusty Bowers</a>, who provided testimony to the January 6 committee during a public hearing earlier this year. Mr Bowers lost to Trump-endorsed candidate David Farnsworth, who said the 2020 election was stolen from the former president. Arizona voters were also choosing between Trump-backed gubernatorial candidate Kari Lake and Taylor Robinson, who has been backed by former vice president Mike Pence. Lake, a former news anchor, said she would not have certified President Joe Biden's statewide victory in 2020 and claimed without evidence that fraud has already occurred during early voting. Democratic “Squad” members Rashida Tlaib of Michigan and Cori Bush of Missouri both sailed through their primary elections on Tuesday night in a victory for progressives. Ms Tlaib easily won her primary against three challengers, receiving more than two-thirds of the vote. Her Squad colleague, Ms Bush, trounced her moderate challenger by taking nearly 70 per cent of the vote. Ms Bush became Missouri's first black congresswoman in 2020. <i>Reuters contributed to this report</i>