let Y, X be non empty set ; :: thesis: for F being BinOp of X
for f being Function of Y,X
for g being Function of X,X holds (F .: g,(id X)) * f = F .: (g * f),f
let F be BinOp of X; :: thesis: for f being Function of Y,X
for g being Function of X,X holds (F .: g,(id X)) * f = F .: (g * f),f
let f be Function of Y,X; :: thesis: for g being Function of X,X holds (F .: g,(id X)) * f = F .: (g * f),f
let g be Function of X,X; :: thesis: (F .: g,(id X)) * f = F .: (g * f),f
thus (F .: g,(id X)) * f = F .: (g * f),((id X) * f) by Th31
.= F .: (g * f),f by FUNCT_2:23 ; :: thesis: verum