Firefighter Stephen Hunt got into difficulty inside the building at around 8.35pm, along with another firefighter, Greater Manchester Fire and Rescue Service said.
Both were pulled out by their colleagues and treated by the Ambulance Service before being taken to hospital.
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Thousands of demonstrators have marched through Boston in opposition to a right-wing rally in the city which was eventually cut short.
Some 1,000 counter-protesters blocked 500 neo-Nazi demonstrators as they tried to march to the site of the death of Hitler ally Rudolf Hess.
Clear skies and lighter winds will bring a chilly night for many