let C be Cocartesian_category; for a, b being Object of C holds [$(in1 (a,b)),(in2 (a,b))$] = id (a + b)
let a, b be Object of C; [$(in1 (a,b)),(in2 (a,b))$] = id (a + b)
A1:
Hom (b,(a + b)) <> {}
by Th61;
then A2:
(id (a + b)) * (in2 (a,b)) = in2 (a,b)
by CAT_1:28;
A3:
Hom (a,(a + b)) <> {}
by Th61;
then
(id (a + b)) * (in1 (a,b)) = in1 (a,b)
by CAT_1:28;
hence
[$(in1 (a,b)),(in2 (a,b))$] = id (a + b)
by A3, A1, A2, Def28; verum