let X be non empty set ; :: thesis: for Y being set
for F being BinOp of X
for f being Function of Y,X
for x being Element of X holds (F [;] (x,(id X))) * f = F [;] (x,f)
let Y be set ; :: thesis: for F being BinOp of X
for f being Function of Y,X
for x being Element of X holds (F [;] (x,(id X))) * f = F [;] (x,f)
let F be BinOp of X; :: thesis: for f being Function of Y,X
for x being Element of X holds (F [;] (x,(id X))) * f = F [;] (x,f)
let f be Function of Y,X; :: thesis: for x being Element of X holds (F [;] (x,(id X))) * f = F [;] (x,f)
let x be Element of X; :: thesis: (F [;] (x,(id X))) * f = F [;] (x,f)
thus (F [;] (x,(id X))) * f = F [;] (x,((id X) * f)) by Th34
.= F [;] (x,f) by FUNCT_2:17 ; :: thesis: verum