let A be Category; :: thesis: for f being Morphism of A holds (id (cod f)) (*) f = f
let f be Morphism of A; :: thesis: (id (cod f)) (*) f = f
reconsider f9 = f as Morphism of dom f, cod f by CAT_1:4;
A1: Hom ((dom f),(cod f)) <> {} by CAT_1:2;
Hom ((cod f),(cod f)) <> {} ;
hence (id (cod f)) (*) f = (id (cod f)) * f9 by A1, CAT_1:def 13
.= f by A1, CAT_1:28 ;
:: thesis: verum