let X, Y be non empty set ; :: thesis: for F being BinOp of X
for f being Function of Y,X
for x being Element of X
for y being Element of Y holds (F [:] f,x) . y = F . (f . y),x
let F be BinOp of X; :: thesis: for f being Function of Y,X
for x being Element of X
for y being Element of Y holds (F [:] f,x) . y = F . (f . y),x
let f be Function of Y,X; :: thesis: for x being Element of X
for y being Element of Y holds (F [:] f,x) . y = F . (f . y),x
let x be Element of X; :: thesis: for y being Element of Y holds (F [:] f,x) . y = F . (f . y),x
let y be Element of Y; :: thesis: (F [:] f,x) . y = F . (f . y),x
dom (F [:] f,x) = Y by FUNCT_2:def 1;
hence (F [:] f,x) . y = F . (f . y),x by Th35; :: thesis: verum