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US President Barack Obama delivers a live televised address to the nation on his plans for military action against the Islamic State, from the Cross Hall of the White House in Washington September 10, 2014.

President Barack Obama would seek to overthrow the regime of Bashar al-Assad if American planes were attacked upon entering Syrian air space, Peter Baker of The New York Times reports .

If Assad's troops f ired at American planes entering Syrian airspace, "Obama said he would order American forces to wipe out Syria’s air defense system," Baker reports. "He went on to say that such an action by Mr. Assad would lead to his overthrow, according to one account."

On Wednesday, Obama announced that he had authorized US airstrikes in Syria while laying out a four-part strategy to "destroy" and "eradicate" radical ISIS militants who have captured roughly a third of Syria and a third of Iraq.

Since August, US warplanes have backed Iraqi soldiers, Kurdish peshmerga fighters, and Iranian-backed Shia militiamen as they attempt to roll back ISIS gains in Iraq.

Baker, who spoke with 10 people who spoke to the president leading up to his speech on Wednesday, writes that Obama " struck his guests as less certain about the endgame on the Syrian side, where he has called for Mr. Assad to step down and must now rely on the same moderate Syrian rebels he refused to arm in the past."

Syrian rebels associated with the Western-backed Free Syrian Army (FSA) have scoffed at Obama's plan, saying that it rushes to target ISIS while ignoring Assad.

"I don't really understand this sudden fuss about ISIS," one FSA fighter told The Guardian. "They killed people, but Bashar has been killing for the last three years. But nobody seems to be interested in that anymore."

Opposition fighters note that simply bombing ISIS will not stop the criminal army and that a comprehensive plan is needed to deal with both ISIS and Assad.

"Instead of bombing ISIS from the air, we need support inside Syria to fight. It's the only way," Mohammed Al Bakhour, 31, a senior commander of an Aleppo-based FSA battalion, told the Guardian . "Once Assad is gone, we'll deal with ISIS ourselves."

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It's unclear if the US would protect what it calls "the legitimate opposition" near Aleppo, Syria's largest city and the last place that the FSA has a significant foothold. FSA-aligned revolutionaries are currently fighting for their survival as ISIS and Assad attack them from all sides.

Helping FSA rebels against Assad's warplanes would force Obama to get involved in " somebody else's civil war " while putting American planes in the sights of Syrian planes and air defense systems.