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 Th66;
then A2:
(id (a + b)) * (in2 a,b) = in2 a,b
by CAT_1:57;
A3:
Hom a,(a + b) <> {}
by Th66;
then
(id (a + b)) * (in1 a,b) = in1 a,b
by CAT_1:57;
hence
[$(in1 a,b),(in2 a,b)$] = id (a + b)
by A3, A1, A2, Def29; verum