(CNN) — Former President Donald Trump and House Speaker Mike Johnson raised concerns Friday about the integrity of U.S. elections in a joint appearance at Mar-a-Lago that featured false claims about voting, immigration and other topics.

Trump’s team billed the event as being about “election integrity” – a phrase he often uses to describe the lie that the 2020 election was rigged, as well as his unfounded claims about future mass voter fraud.

Here’s a breakdown of some of the false claims from their remarks.

Johnson raises baseless concerns on noncitizen voting

House Speaker Mike Johnson raised baseless concerns about “potentially hundreds of thousands of votes” being cast by undocumented immigrants in the November presidential election.

“If an individual only asserts or simply states that they are a citizen, they don’t have to prove it, and they can register that person to vote in a federal election,” Johnson said, adding that “we only want US citizens to vote in U.S. elections.”

To solve this issue, which he called a “serious problem,” Johnson said House Republicans would propose a bill that requires people to directly provide proof of U.S. citizenship when registering to vote for federal elections.

Facts First: The system, as it is currently set up, is working, and effectively prevents mass voting by non-citizens in U.S. elections. Despite Johnson’s focus on this topic, it is extremely rare, according to decades of voting data and nonpartisan experts. It’s so uncommon that voting experts don’t see it as a problem plaguing U.S. elections.

In federal and state elections, where voting by non-citizens is illegal, it occurs on a microscopic level. (It’s true that a handful of municipalities have passed laws letting non-citizens participate in local elections, like for school board. But this wasn’t the focus of Johnson’s concerns about federal elections.)

When people register to vote, they must provide a driver’s license or social security number, and their identity is checked against existing databases. Voters are required to swear under penalty of perjury that they are a U.S. citizen, and multiple federal laws make it illegal for non-citizens to vote, which can lead to imprisonment or deportation.

This system, as shown from decades of data, is very effective at stopping non-citizens from registering and voting in federal elections.

“It happens almost never,” said David Becker, founder of the nonpartisan Center for Election Innovation & Research. “Making something illegal doesn’t stop it from happening, but we know how often it happens, and it’s extremely rare. This is a problem that is very small. And it has almost always occurred because of a misunderstanding.”

The right-leaning Heritage Foundation’s database of confirmed fraud cases lists less than 100 examples of non-citizens voting between 2002 and 2022, amid more than one billion lawfully cast ballots. And the left-leaning Brennan Center for Justice analyzed more than 23 million votes from the 2016 election and found an estimated 30 examples.

Further, from a common-sense perspective, there’s little to gain for an undocumented immigrant who theoretically wants to vote in a presidential election. There’s almost no chance their single ballot would tip the results, and they’d be risking everything to do it.

“The penalties are high, and the payoff is low,” said Rick Hasen, an election law expert at the UCLA School of Law. “If you aren’t a citizen and you vote, and you’re caught, you can face deportation and criminal penalties. And your chances of affecting an election outcome are small. It’s very unlikely someone would purposely choose to vote as a noncitizen.”

Hasen, a Trump critic, said, “if we had a big problem in this country with non-citizen voting, maybe that would justify more than an affidavit, swearing to their citizenship status. But because we don’t have a big problem, we don’t need to put impediments in the path of more than 99% of voters who are qualified.

Trump has a long history of spreading false claims about foreign nationals voting in U.S. elections. Most famously, he claimed “millions” of undocumented immigrants cast ballots in 2016, a brazen lie that he used to explain why he lost the popular vote to Democratic nominee Hillary Clinton.

From CNN’s Marshall Cohen 

Trump claims that ‘millions’ of migrants are coming from the Congo, Venezuela, mental institutions

Trump claimed that “millions and millions” of people, including terrorists and people from jails and mental institutions have come illegally to the United States from countries like Venezuela and “the Congo.”

Facts First: There is no evidence for Trump’s repeated claims that any coutries, much less “the Congo” and Venezuela, have emptied prisons and mental health institutions to allow violent criminals to come to the U.S. border as migrants.

Last year, Trump’s campaign was unable to provide any evidence for his narrower claim at the time that South American countries were emptying mental health facilities to somehow dump patients upon the U.S. Experts on the Democratic Republic of Congo and the Republic of Congo, plus both pro-immigration and anti-immigration organizations in the United States have also told CNN they have not seen any evidence of Congolese prisons being emptied.

From CNN’s Piper Hudspeth Blackburn and Daniel Dale

Trump falsely claimed Biden is orchestrating the criminal trial against him

Trump baselessly claimed – as he often does – that Biden is secretly orchestrating the New York state criminal case against him, which is set to go to trial on Monday.

“That is election interference by the Biden administration,” Trump said. “They actually took their top guy, one of their top guys, put him into the D.A.’s office to run it, and it is a shame.”

Trump is referring to the fact that Matthew Colangelo, who had served as a senior Justice Department official under Biden, left the department in 2022 for a job in the office of the Manhattan District Attorney who is prosecuting the case, Alvin Bragg.

Facts First: There is no basis for Trump’s claims that the trials against him have been directed by Biden in an effort to interfere with the election.

First, there is no evidence that Biden, his White House or his Justice Department has had any role in launching or running Bragg’s case, let alone that Biden operatives are issuing secret commands in the case – and Bragg is a locally elected official who does not report to the federal government.

There is also no evidence the White House or the Biden administration had anything to do with Colangelo’s decision to leave the Justice Department and join the district attorney’s office as senior counsel to Bragg; Colangelo and Bragg had been colleagues before Bragg was elected Manhattan district attorney in 2021.

From CNN’s Marshall Cohen and Daniel Dale

Trump inflates border crossing numbers

Trump said “millions and millions of people are pouring in (to the U.S.) … We probably have 15 million (migrants).”

Facts First: Trump’s figure about how many migrants have crossed the border under the Biden administration is inflated.  

As of March, U.S. Customs and Border Protection has recorded nearly 9.4 million border encounters nationwide since President Joe Biden took office in January 2021.

While millions of people are not “pouring” into the United States at one time, the nation continues to grapple with a migrant surge at the southern border.

From CNN’s Danya Gainor

Trump claims that ‘every legal scholar’ wanted Roe v. Wade overturned

At an appearance in Mar A Lago with House Speaker Mike Johnson, former President Donald Trump touted that “we broke Roe V. Wade” and claimed that every “legal scholar” wanted it overturned.

Facts First: Trump’s claim that “every legal scholar” wanted Roe overturned is not true. Many wanted Roe preserved, as several legal scholars reiterated in comments to CNN earlier this week.

Read more from those legal scholars here.

From CNN’s Daniel Dale and Piper Hudspeth Blackburn