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

now

let x be Element of A; :: thesis: ((ComplexFuncMult A) . f,g) . x = ((ComplexFuncMult A) . g,f) . x
thus ((ComplexFuncMult A) . f,g) . x = (g . x) * (f . x) by Th2
.= ((ComplexFuncMult A) . g,f) . x by Th2 ; :: thesis: verum

end;

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