let C be Category; :: thesis: for a, b being Object of C
for f being Morphism of a,b st Hom (a,b) <> {} holds
(id b) * f = f
let a, b be Object of C; :: thesis: for f being Morphism of a,b st Hom (a,b) <> {} holds
(id b) * f = f
let f be Morphism of a,b; :: thesis: ( Hom (a,b) <> {} implies (id b) * f = f )
assume A1: Hom (a,b) <> {} ; :: thesis: (id b) * f = f
A2: (id b) (*) f = f by A1, Def10;
Hom (b,b) <> {} ;
hence (id b) * f = f by A1, A2, Def11; :: thesis: verum