Peter Bergen is CNN's national security analyst, a vice president at New America and a professor of practice at Arizona State University. He is the author of " United States of Jihad: Investigating America's Homegrown Terrorists ."

(CNN) On Tuesday, US-backed forces announced that Raqqa, the de facto capital of ISIS in Syria, had fallen.

President Donald Trump quickly took a victory lap during an interview the same day, stating that ISIS hadn't been defeated earlier because "you didn't have Trump as your president."

Is this claim true? Not really, according to US military officials.

In August 2016, Lt. Gen. Sean MacFarland, who was the ground commander for the fight against ISIS, said the US-led coalition had killed an estimated 45,000 ISIS fighters.

About a year later, at the Aspen Security Forum in July 2017, the commander of the US Special Operations Command, Gen. Raymond "Tony" Thomas, said that an estimated 60,000 to 70,000 ISIS fighters had been killed since the US-led campaign against the terror group began in August 2014.

Ergo, according to these senior US military officials, the bulk of ISIS fighters were killed during the pre-Trump period.

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That shouldn't be too surprising. After all, the campaign to eradicate ISIS began two and a half years before Trump assumed office.

The operation to take back Mosul, the second-largest city in Iraq where ISIS had first declared its "caliphate," began in October 2016 while President Barack Obama was still in office and had been long-planned.

Shortly after the Mosul operation was launched, Gen. Joseph Votel, the commander of US Central Command, which oversees the wars in Iraq and Syria, told me : "We have been doing preparatory stuff against Raqqa and Mosul for a long time, long before we said, 'the assault on Mosul has begun.' We have taken out 36 ISIS leaders in the Mosul area; to me that is part of the preparation phase."

Under Obama, ISIS also lost significant Iraqi cities such as Falluja Ramadi and Tikrit

To be sure, Trump loosened the "rules of engagement" for the US military, enabling ground commanders to more easily carry out operations without having to seek permission up the chain of command, but these are tactical changes -- not strategic game changers.

According to the UK-based Airwars, which carefully tracks coalition airstrikes in Iraq and Syria, the numbers of strikes has declined in Iraq under Trump, while they have spiked in Syria.

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Significantly, in May, Trump approved a plan to arm the Kurdish forces fighting ISIS in Syria. Turkey strenuously objected to this plan because of its restive Kurdish population, but the Trump administration went ahead anyway. These are the Kurdish forces that helped to liberate Raqqa on Tuesday.

Bottom line: There is much continuity between the Obama campaign plan against ISIS and the Trump plan.

Also, Trump needs to be careful about taking too much of a victory lap when it comes to ISIS. He could fall into the same trap that Obama did when he observed in early 2014 that ISIS was a "JV team" -- meaning junior varsity team, made up of younger, less-experienced players.

The political conditions in the Middle East that gave rise to ISIS -- the sectarian and ethnic conflicts around the region and the collapse of Arab governments and economies -- will surely engender a son of ISIS. And even a deeply wounded ISIS can continue to inspire attacks in the West.