let C, D be Category; :: thesis: for F being Function of the carrier' of C, the carrier' of D
for f being Morphism of C holds ((*' F) *') . (f opp) = (F . f) opp
let F be Function of the carrier' of C, the carrier' of D; :: thesis: for f being Morphism of C holds ((*' F) *') . (f opp) = (F . f) opp
let f be Morphism of C; :: thesis: ((*' F) *') . (f opp) = (F . f) opp
thus ((*' F) *') . (f opp) = (F . (opp (f opp))) opp by Lm17
.= (F . f) opp ; :: thesis: verum