let A, B be Category; :: thesis: for F, F1, F2 being Functor of A,B st F is_transformable_to F1 & F1 is_transformable_to F2 holds
F is_transformable_to F2
let F, F1, F2 be Functor of A,B; :: thesis: ( F is_transformable_to F1 & F1 is_transformable_to F2 implies F is_transformable_to F2 )
assume A1: ( F is_transformable_to F1 & F1 is_transformable_to F2 ) ; :: thesis: F is_transformable_to F2
let a be Object of A; :: according to NATTRA_1:def 2 :: thesis: Hom (F . a),(F2 . a) <> {}
( Hom (F . a),(F1 . a) <> {} & Hom (F1 . a),(F2 . a) <> {} ) by A1, Def2;
hence Hom (F . a),(F2 . a) <> {} by CAT_1:52; :: thesis: verum