let A, B be Category; :: thesis: for F1, F2 being Functor of A,B st F1 is_transformable_to F2 holds
for t being transformation of F1,F2
for a being Object of A holds t . a in Hom ((F1 . a),(F2 . a))
let F1, F2 be Functor of A,B; :: thesis: ( F1 is_transformable_to F2 implies for t being transformation of F1,F2
for a being Object of A holds t . a in Hom ((F1 . a),(F2 . a)) )
assume A1: F1 is_transformable_to F2 ; :: thesis: for t being transformation of F1,F2
for a being Object of A holds t . a in Hom ((F1 . a),(F2 . a))
let t be transformation of F1,F2; :: thesis: for a being Object of A holds t . a in Hom ((F1 . a),(F2 . a))
let a be Object of A; :: thesis: t . a in Hom ((F1 . a),(F2 . a))
Hom ((F1 . a),(F2 . a)) <> {} by A1;
hence t . a in Hom ((F1 . a),(F2 . a)) by CAT_1:def 5; :: thesis: verum