let f be PartFunc of (REAL 2),REAL ; :: thesis: for z0 being Element of REAL 2 st f is_hpartial_differentiable`11_in z0 holds
SVF1 1,(pdiff1 f,1),z0 is_continuous_in (proj 1,2) . z0
let z0 be Element of REAL 2; :: thesis: ( f is_hpartial_differentiable`11_in z0 implies SVF1 1,(pdiff1 f,1),z0 is_continuous_in (proj 1,2) . z0 )
assume f is_hpartial_differentiable`11_in z0 ; :: thesis: SVF1 1,(pdiff1 f,1),z0 is_continuous_in (proj 1,2) . z0
then pdiff1 f,1 is_partial_differentiable_in z0,1 by Th9;
hence SVF1 1,(pdiff1 f,1),z0 is_continuous_in (proj 1,2) . z0 by PDIFF_2:21; :: thesis: verum