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

now

let x be Element of A; :: thesis: ((ComplexFuncAdd A) . f,g) . x = ((ComplexFuncAdd A) . g,f) . x
thus ((ComplexFuncAdd A) . f,g) . x = (g . x) + (f . x) by Th1
.= ((ComplexFuncAdd A) . g,f) . x by Th1 ; :: thesis: verum

end;

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