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 Th48
.= F . (g . x),x by FUNCT_1:35 ; :: thesis: verum