let A be Category; for a, b being Object of A st Hom (a,b) <> {} holds
for f being Morphism of a,b holds (id A) /. f = f
let a, b be Object of A; ( Hom (a,b) <> {} implies for f being Morphism of a,b holds (id A) /. f = f )
assume A1:
Hom (a,b) <> {}
; for f being Morphism of a,b holds (id A) /. f = f
let f be Morphism of a,b; (id A) /. f = f
thus (id A) /. f =
(id A) . f
by A1, CAT_3:def 10
.=
f
by FUNCT_1:18
; verum