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) <> {} & t . a is Morphism of F1 . a,F2 . a ) by A1, NATTRA_1:def 2;
hence t . a in Hom (F1 . a),(F2 . a) by CAT_1:def 7; :: thesis: verum