let A be non empty set ; :: thesis: for f, g being Element of PFuncs A,REAL holds (addpfunc A) . f,g = (addpfunc A) . g,f
let f, g be Element of PFuncs A,REAL ; :: thesis: (addpfunc A) . f,g = (addpfunc A) . g,f
addpfunc A is commutative by RFUNCT_3:16;
hence (addpfunc A) . f,g = (addpfunc A) . g,f by BINOP_1:def 2; :: thesis: verum