theorem Th12: :: PDIFF_5:12

for x0, y0, z0 being Real
for u being Element of REAL 3
for f being PartFunc of (REAL 3),REAL st u = <*x0,y0,z0*> & f is_hpartial_differentiable`13_in u holds
hpartdiff13 (f,u) = diff ((SVF1 (3,(pdiff1 (f,1)),u)),z0)