theorem :: NDIFF_7:48

for X, Y, W being RealNormSpace
for Z being Subset of [:X,Y:]
for f, g being PartFunc of [:X,Y:],W st Z is open & f is_partial_differentiable_on`2 Z & g is_partial_differentiable_on`2 Z holds
( f - g is_partial_differentiable_on`2 Z & (f - g) `partial`2| Z = (f `partial`2| Z) - (g `partial`2| Z) )