let X, Y be non empty set ; :: thesis: for F being BinOp of X

for f being Function of Y,X holds (F .: ((id X),(id X))) * f = F .: (f,f)

let F be BinOp of X; :: thesis: for f being Function of Y,X holds (F .: ((id X),(id X))) * f = F .: (f,f)

let f be Function of Y,X; :: thesis: (F .: ((id X),(id X))) * f = F .: (f,f)

thus (F .: ((id X),(id X))) * f = F .: (((id X) * f),((id X) * f)) by Th25

.= F .: (((id X) * f),f) by FUNCT_2:17

.= F .: (f,f) by FUNCT_2:17 ; :: thesis: verum

for f being Function of Y,X holds (F .: ((id X),(id X))) * f = F .: (f,f)

let F be BinOp of X; :: thesis: for f being Function of Y,X holds (F .: ((id X),(id X))) * f = F .: (f,f)

let f be Function of Y,X; :: thesis: (F .: ((id X),(id X))) * f = F .: (f,f)

thus (F .: ((id X),(id X))) * f = F .: (((id X) * f),((id X) * f)) by Th25

.= F .: (((id X) * f),f) by FUNCT_2:17

.= F .: (f,f) by FUNCT_2:17 ; :: thesis: verum