let f1, f2 be Function of COMPLEX,COMPLEX; :: thesis: ( ( for z being Complex holds f1 . z = Sum (z ExpSeq) ) & ( for z being Complex holds f2 . z = Sum (z ExpSeq) ) implies f1 = f2 )
assume A2: for z being Complex holds f1 . z = Sum (z ExpSeq) ; :: thesis: ( ex z being Complex st not f2 . z = Sum (z ExpSeq) or f1 = f2 )
assume A3: for z being Complex holds f2 . z = Sum (z ExpSeq) ; :: thesis: f1 = f2
for z being Element of COMPLEX holds f1 . z = f2 . z

proof

let z be Element of COMPLEX ; :: thesis: f1 . z = f2 . z
thus f1 . z = Sum (z ExpSeq) by A2
.= f2 . z by A3 ; :: thesis: verum

end;

hence f1 = f2 ; :: thesis: verum