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