let C be Category; :: thesis: for a, b being Object of C
for f being Morphism of a,b st Hom (a,b) <> {} holds
f opp is Morphism of b opp ,a opp
let a, b be Object of C; :: thesis: for f being Morphism of a,b st Hom (a,b) <> {} holds
f opp is Morphism of b opp ,a opp
let f be Morphism of a,b; :: thesis: ( Hom (a,b) <> {} implies f opp is Morphism of b opp ,a opp )
assume Hom (a,b) <> {} ; :: thesis: f opp is Morphism of b opp ,a opp
then f in Hom (a,b) by CAT_1:def 4;
then f opp in Hom ((b opp),(a opp)) by Th13;
hence f opp is Morphism of b opp ,a opp by CAT_1:def 4; :: thesis: verum