let B, A be Category; :: thesis: for F1, F2 being Functor of A,B st F1 is_transformable_to F2 holds
for t1, t2 being transformation of F1,F2 st ( for a being Object of A holds t1 . a = t2 . a ) holds
t1 = t2
let F1, F2 be Functor of A,B; :: thesis: ( F1 is_transformable_to F2 implies for t1, t2 being transformation of F1,F2 st ( for a being Object of A holds t1 . a = t2 . a ) holds
t1 = t2 )
assume A1: F1 is_transformable_to F2 ; :: thesis: for t1, t2 being transformation of F1,F2 st ( for a being Object of A holds t1 . a = t2 . a ) holds
t1 = t2
let t1, t2 be transformation of F1,F2; :: thesis: ( ( for a being Object of A holds t1 . a = t2 . a ) implies t1 = t2 )
assume A2: for a being Object of A holds t1 . a = t2 . a ; :: thesis: t1 = t2

now

let a be Object of A; :: thesis: t1 . a = t2 . a
thus t1 . a = t1 . a by A1, Def5
.= t2 . a by A2
.= t2 . a by A1, Def5 ; :: thesis: verum

end;

hence t1 = t2 by FUNCT_2:113; :: thesis: verum