let C be Category; :: thesis: for a, b being Object of C
for f being Morphism of a,b st a is initial holds
init a,b = f
let a, b be Object of C; :: thesis: for f being Morphism of a,b st a is initial holds
init a,b = f
let f be Morphism of a,b; :: thesis: ( a is initial implies init a,b = f )
assume A1: a is initial ; :: thesis: init a,b = f
then Hom a,b <> {} by CAT_1:def 16;
then ( dom f = a & cod f = b ) by CAT_1:23;
hence init a,b = f by A1, Th43; :: thesis: verum