let F1, F2 be set ; :: thesis: ( ( for x being set holds
( x in F1 iff x is Functor of C,D ) ) & ( for x being set holds
( x in F2 iff x is Functor of C,D ) ) implies F1 = F2 )
assume that
A3: for x being set holds
( x in F1 iff x is Functor of C,D ) and
A4: for x being set holds
( x in F2 iff x is Functor of C,D ) ; :: thesis: F1 = F2

now :: thesis: for x being set holds
( x in F1 iff x in F2 )

let x be set ; :: thesis: ( x in F1 iff x in F2 )
( x in F1 iff x is Functor of C,D ) by A3;
hence ( x in F1 iff x in F2 ) by A4; :: thesis: verum

end;

hence F1 = F2 by TARSKI:1; :: thesis: verum