theorem Th32: :: CFCONT_1:32

for x0 being Complex
for f being PartFunc of COMPLEX,COMPLEX holds
( f is_continuous_in x0 iff ( x0 in dom f & ( for r being Real st 0 < r holds
ex s being Real st
( 0 < s & ( for x1 being Complex st x1 in dom f & |.(x1 - x0).| < s holds
|.((f /. x1) - (f /. x0)).| < r ) ) ) ) )