for m, n being non zero Nat
for i being Nat
for f1, f2 being PartFunc of (REAL-NS m),(REAL-NS n)
for x being Point of (REAL-NS m) st f1 is_partial_differentiable_in x,i & f2 is_partial_differentiable_in x,i holds
( f1 - f2 is_partial_differentiable_in x,i & partdiff ((f1 - f2),x,i) = (partdiff (f1,x,i)) - (partdiff (f2,x,i)) )