“It was nearly 10 years ago that a bright September day was darkened by the worst attack on the American people in our history,” Barack Obama said in a televised address, as the news emerged of Osama Bin Laden’s discovery and subsequent shooting dead in Pakistan. “The images of 9/11 are seared into our national memory.”

A year later, in re-election mode, Obama and his deputy Joe Biden would be criticised for making use of the special forces’ operation in a campaign ad, with the vice president going as far as to question wether the president’s rival, Mitt Romney, had what it took to order the high-risk operation.

“On this gut issue, we know what president Obama did. We can’t say for certain what governor Romney would have done,” Biden, who is among those wanting to take on Donald Trump in 2020, said in a speech, suggesting their re-election slogan should have been “Bin Laden is dead and General Motors is alive”.

The circumstances of Trump’s declaration that Isis leader Abu Bakr al-Baghdadi had been killed in US military raid in Syria bore many similarities to Obama’s announcement.

Stylistically, there were some points of divergence; Obama did not use the word “whimpering” six times, and it was a different supposed ally, Pakistan rather than Turkey, that could not be trusted to keep secret the operation. Bin Laden was shot dead by Navy SEALs, while Baghdadi killed himself as Delta force soldiers closed in on him.

What is also similar is that Trump will use the death of the Isis chief to boost his re-election chances, just as Obama did with the killing of the Al-Qaeda leader. Already, the White House has released an image of Trump watching stern-faced with his top generals as the operation unfolded, just as Obama did.

“The United States has been searching for Baghdadi for many years,” Trump said on Sunday morning, from the White House’s Diplomatic Reception Room. “Capturing or killing Baghdadi has been the top national security priority of my administration.”

He added: “Baghdadi has been on the run for many years, long before I took office. But at my direction, as commander-in-chief of the United States, we obliterated his caliphate, 100 per cent, in March of this year.”

The killing of Baghdadi undoubtedly helps Trump’s re-election bid. A tough, military-led counterterrorism stance is something that appeals to many Americans, especially one that results in the death of a man whose organisation executed four US hostages and posted the horror on the internet.

In a nod to the large number of evangelicals who voted for him in 2016, Trump was careful in his speech to point out that Isis was responsible for the deaths of large numbers of Christians, and other religious minorities, in the Middle East.

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And in what may have been an attempt to repair some of the anguish felt by those Republicans angry about his earlier decision to withdraw US forces from northern Syria and abandon its Kurdish allies, Trump praised the role of the Syrian Kurds in helping locate Baghdadi. (He also praised the governments of Russia, Syria, Turkey and Iraq. Moscow said on Monday the operation will be an asset to Trump.)

What is less clear, is how much Baghdadi’s death helps Trump’s 2020 fortunes. His approval rating, as collated by Real Clear Politics, stands at just 41 points, which is perilously low for a president seeking re-election. We can expect that to push up a few points in the coming days, as new polling is reflected.

The trouble for the president is that most Americans have already made their mind up about him, and that the number of independent voters left to be won over is small.

Yet, Trump won his way to the narrowest of victories by around 70,000 votes spread over three states in the upper midwest – Wisconsin, Michigan and Pennsylvania. He and his campaign manager, Brad Parscale, are using hundreds of millions of dollars to try and win every vote, and the death of Baghdadi will likely be featured heavily in that campaign.

In that sense, the comparison to watch may be less Obama’s re-election strategy in 2012, than George W Bush in 2004. In that case, the Republicans had a candidate whose mangling of foreign names made Trump’s rendering of "Abu Bakr al-Baghdadi" sound like that of a BBC newsreader.

Bush was a deeply divisive president who had just launched an unpopular war in the Middle East, and who, in John Kerry faced a Democrat challenger, who unlike the president, had a record of active duty in the military. Under the direction of political adviser Karl Rove, Bush and his vow of capturing Bin Laden “dead or alive”, made it over the finishing line with a popular vote victory of 51-48.

Trump too will be hoping he can do the same, and that some of Rove’s magic rubs off on him.

“Last night was a great night for the United States and for the world,” he said on Sunday.