let C be Category; :: thesis: for b, a being Object of C st b is terminal holds
( dom (term (a,b)) = a & cod (term (a,b)) = b )
let b, a be Object of C; :: thesis: ( b is terminal implies ( dom (term (a,b)) = a & cod (term (a,b)) = b ) )
assume b is terminal ; :: thesis: ( dom (term (a,b)) = a & cod (term (a,b)) = b )
then Hom (a,b) <> {} by CAT_1:def 12;
hence ( dom (term (a,b)) = a & cod (term (a,b)) = b ) by CAT_1:5; :: thesis: verum