let C be Category; :: thesis: for a, b being Object of C
for f being Morphism of a,b st b is terminal holds
term a,b = f
let a, b be Object of C; :: thesis: for f being Morphism of a,b st b is terminal holds
term a,b = f
let f be Morphism of a,b; :: thesis: ( b is terminal implies term a,b = f )
assume A1: b is terminal ; :: thesis: term a,b = f
then Hom a,b <> {} by CAT_1:def 15;
then ( dom f = a & cod f = b ) by CAT_1:23;
hence term a,b = f by A1, Th40; :: thesis: verum