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

( 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 object holds

( x in F1 iff x in F2 )

hence
F1 = F2
by TARSKI:2; :: thesis: verum( x in F1 iff x in F2 )

let x be object ; :: 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;( x in F1 iff x is Functor of C,D ) by A3;

hence ( x in F1 iff x in F2 ) by A4; :: thesis: verum