let X be non empty set ; :: thesis: for F being BinOp of X

for x being Element of X holds (F [;] (x,(id X))) . x = F . (x,x)

let F be BinOp of X; :: thesis: for x being Element of X holds (F [;] (x,(id X))) . x = F . (x,x)

let x be Element of X; :: thesis: (F [;] (x,(id X))) . x = F . (x,x)

thus (F [;] (x,(id X))) . x = F . (x,((id X) . x)) by Th53

.= F . (x,x) ; :: thesis: verum

for x being Element of X holds (F [;] (x,(id X))) . x = F . (x,x)

let F be BinOp of X; :: thesis: for x being Element of X holds (F [;] (x,(id X))) . x = F . (x,x)

let x be Element of X; :: thesis: (F [;] (x,(id X))) . x = F . (x,x)

thus (F [;] (x,(id X))) . x = F . (x,((id X) . x)) by Th53

.= F . (x,x) ; :: thesis: verum