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(CNN) —  

Since the early days of special counsel Robert Mueller’s investigation, President Donald Trump has not only claimed innocence but has argued that the entire investigation is “illegal.”

Trump repeated the same argument Friday, tweeting that the investigation “was an illegal & conflicted investigation in search of a crime.” In June 2018, Trump claimed “the appointment of the Special Counsel is totally UNCONSTITUTIONAL!”

Facts First: This is wrong – multiple court rulings have upheld Mueller’s appointment, his authority, and the decisions he’s made.

A handful of defendants and witnesses ensnarled in the investigation have unsuccessfully tried to invalidate Mueller’s authority. Amid this barrage of legal challenges, four trial-level judges and two panels of appeals court judges have ruled in Mueller’s favor.

The judges who handed down these decisions were appointed to the federal bench by Democratic and Republican presidents. Here’s a breakdown of some of their decisions:

-Trump’s former campaign chairman Paul Manafort argued that Mueller’s probe was unconstitutional. Manafort said that Deputy Attorney General Rod Rosenstein did not give Mueller the authority to bring financial criminal charges against him, because they were not connected to his work as Trump’s campaign chairman.

Federal judge T.S. Ellis rejected these efforts – even after publicly criticizing Mueller’s approach of targeting Manafort – writing that “no interpretive gymnastics are necessary to determine that the investigation at issue here falls within” the authority of Mueller’s investigation.

-In a separate criminal case against him, Manafort and his lawyers made the same argument. Mueller’s investigation was outside of its legal authority because the original appointment order was too wide-ranging, they claimed.

Federal judge Amy Berman Jackson dismissed this argument, writing that it was within Mueller’s investigation to look into Manafort’s connections with Ukraine and Russia during his investigation into Russia and the Trump campaign. In an opinion, Jackson wrote “the Special Counsel would have been remiss to ignore such an obvious potential link between the Trump campaign and the Russian government.”

-Concord Management and Consulting, a Russian company Mueller’s team says operated a “troll farm” that produced political propaganda online during the 2016 campaign, was charged last year with conspiring to defraud the US government by interfering with the Federal Election Commission, the Justice Department and the State Department. The company has pleaded not guilty.

Federal judge Dabney Friedrich of the US District Court in DC, sided with Mueller’s team and rejected Concord’s argument that Mueller’s investigation was unconstitutional. “The appointment does not violate core separation-of-powers principles,” Friedrich wrote in an opinion last August. “Nor has the Special Counsel exceeded his authority under the appointment order by investigating and prosecuting Concord.” Judge Fredrich was appointed by Trump.

-Beryl Howell, the chief judge of the DC District Court, has also held two witnesses – a Roger Stone associate and a mystery company owned by a foreign government – in contempt of court for refusing to comply with Mueller’s grand jury subpoenas.

The DC Circuit Court of Appeals weighed in on the question of Mueller’s constitutionality after the Stone associate Andrew Miller appealed. The three-judge panel unanimously agreed Mueller was lawfully appointed under the Constitution as a Justice Department prosecutor. Miller hasn’t indicated if he will continue to fight.

A separate group of judges in the same appeals court heard arguments from a foreign-owned company that hasn’t been identified in court filings. The company claims it shouldn’t have to comply with the criminal investigation or $50,000 a day contempt fines because it’s protected as part of a foreign sovereign entity, but the three judges unanimously disagreed. The Supreme Court is set to review the company’s question on Friday, and hasn’t yet said if high court arguments will take place.

Katelyn Polantz contributed to this report.