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