let X, Y be non empty set ; :: thesis: for F being BinOp of X
for f being Function of Y,X
for x being Element of X holds (F [:] ((id X),x)) * f = F [:] (f,x)
let F be BinOp of X; :: thesis: for f being Function of Y,X
for x being Element of X holds (F [:] ((id X),x)) * f = F [:] (f,x)
let f be Function of Y,X; :: thesis: for x being Element of X holds (F [:] ((id X),x)) * f = F [:] (f,x)
let x be Element of X; :: thesis: (F [:] ((id X),x)) * f = F [:] (f,x)
thus (F [:] ((id X),x)) * f = F [:] (((id X) * f),x) by Th29
.= F [:] (f,x) by FUNCT_2:17 ; :: thesis: verum