:: deftheorem defines `partial3| PDIFF_4:def 6 :
for f being PartFunc of (REAL 3),REAL
for D being set st f is_partial_differentiable`3_on D holds
for b₃ being PartFunc of (REAL 3),REAL holds
( b₃ = f `partial3| D iff ( dom b₃ = D & ( for u being Element of REAL 3 st u in D holds
b₃ . u = partdiff (f,u,3) ) ) );