let X be non empty set ; :: thesis: for F being BinOp of X
for x being Element of X
for g being Function of X,X holds (F .: (g,(id X))) . x = F . ((g . x),x)
let F be BinOp of X; :: thesis: for x being Element of X
for g being Function of X,X holds (F .: (g,(id X))) . x = F . ((g . x),x)
let x be Element of X; :: thesis: for g being Function of X,X holds (F .: (g,(id X))) . x = F . ((g . x),x)
let g be Function of X,X; :: thesis: (F .: (g,(id X))) . x = F . ((g . x),x)
thus (F .: (g,(id X))) . x = F . ((g . x),((id X) . x)) by Th37
.= F . ((g . x),x) ; :: thesis: verum