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

now

let x be Element of A; :: thesis: ((ComplexFuncMult A) . (ComplexFuncUnit A),f) . x = f . x
thus ((ComplexFuncMult A) . (ComplexFuncUnit A),f) . x = ((ComplexFuncUnit A) . x) * (f . x) by Th2
.= 1r * (f . x) by FUNCOP_1:13
.= f . x by COMPLEX1:def 7 ; :: thesis: verum

end;

hence (ComplexFuncMult A) . (ComplexFuncUnit A),f = f by FUNCT_2:113; :: thesis: verum