let A be Category; :: thesis: for f being Morphism of A holds f * (id (dom f)) = f
let f be Morphism of A; :: thesis: f * (id (dom f)) = f
reconsider f9 = f as Morphism of dom f, cod f by CAT_1:22;
A1: Hom ((dom f),(cod f)) <> {} by CAT_1:19;
Hom ((dom f),(dom f)) <> {} by CAT_1:56;
hence f * (id (dom f)) = f9 * (id (dom f)) by A1, CAT_1:def 13
.= f by A1, CAT_1:58 ;
:: thesis: verum