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Leslie Hughes "struggled up" from his cot to administer artificial respiration to Marine Sergeant Hackett, The Washington Post said.
Another firefighter, Guy Swarthouth, administered oxygen to Hackett, who was "out for about five minutes," said Hughes, who returned to the fireground.
The blaze damaged the Henderson Hall theater building.
Firefighters from Arlington County, Fort Myer and Henderson Hall - supplemented by 200 off-duty Marines - extinguished the flames, the Post reported.