if you subtract any one of the three the fire cannot exist
remove the oxygen and fuel cannot readily burn,
remove the fuel and there is nothing to burn,
and removing the heat takes the enabling catalyst out of the equation.
but always remember the fuel can be anything that can burn!
if you removed the wood or paper and the paint is still on fire you haven't removed all the fuel.
consider what your extinguishing agents are and how they affect the fire.
water cools the fire! dry chemicals, co2, and foams smother or remove oxygen and clearing flammable debris removes the fuel!
removing the fuel is not an expedient way to fight an active fire as it requires a lot more manpower to deal with mass movement, therefore concentrating on knocking the fire down and smothering it gets it under control.