let C be Cartesian_category; :: thesis: for a, b being Object of C
for f being Morphism of a,b st Hom (a,b) <> {} holds
<:f,f:> = (Delta b) * f
let a, b be Object of C; :: thesis: for f being Morphism of a,b st Hom (a,b) <> {} holds
<:f,f:> = (Delta b) * f
let f be Morphism of a,b; :: thesis: ( Hom (a,b) <> {} implies <:f,f:> = (Delta b) * f )
assume A1: Hom (a,b) <> {} ; :: thesis: <:f,f:> = (Delta b) * f
( Hom (b,b) <> {} & (id b) * f = f ) by A1, CAT_1:28;
hence <:f,f:> = (Delta b) * f by A1, Th25; :: thesis: verum