theorem :: NDIFF_4:12

for x0 being Real
for n being non zero Element of NAT
for f1, f2 being PartFunc of REAL,(REAL n) st f1 is_differentiable_in x0 & f2 is_differentiable_in x0 holds
( f1 - f2 is_differentiable_in x0 & diff ((f1 - f2),x0) = (diff (f1,x0)) - (diff (f2,x0)) )