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 Th66
.= F . (x,x) by FUNCT_1:35 ; :: thesis: verum