theorem :: PDIFF_5:63

for r being Real
for u0 being Element of REAL 3
for f being PartFunc of (REAL 3),REAL st f is_hpartial_differentiable`23_in u0 holds
( r (#) (pdiff1 (f,2)) is_partial_differentiable_in u0,3 & partdiff ((r (#) (pdiff1 (f,2))),u0,3) = r * (hpartdiff23 (f,u0)) )