theorem :: PDIFF_3:26

for z0 being Element of REAL 2
for f1, f2 being PartFunc of (REAL 2),REAL st f1 is_hpartial_differentiable`12_in z0 & f2 is_hpartial_differentiable`12_in z0 holds
( (pdiff1 (f1,1)) - (pdiff1 (f2,1)) is_partial_differentiable_in z0,2 & partdiff (((pdiff1 (f1,1)) - (pdiff1 (f2,1))),z0,2) = (hpartdiff12 (f1,z0)) - (hpartdiff12 (f2,z0)) )