let A be non empty set ; :: thesis: for f being Element of Funcs A,COMPLEX holds (ComplexFuncAdd A) . (ComplexFuncZero A),f = f
let f be Element of Funcs A,COMPLEX ; :: thesis: (ComplexFuncAdd A) . (ComplexFuncZero A),f = f

now

let x be Element of A; :: thesis: ((ComplexFuncAdd A) . (ComplexFuncZero A),f) . x = f . x
thus ((ComplexFuncAdd A) . (ComplexFuncZero A),f) . x = ((ComplexFuncZero A) . x) + (f . x) by Th1
.= 0c + (f . x) by FUNCOP_1:13
.= f . x ; :: thesis: verum

end;

hence (ComplexFuncAdd A) . (ComplexFuncZero A),f = f by FUNCT_2:113; :: thesis: verum