let D1, D2 be set ; :: thesis: ( ( for o being object holds
( o in D1 iff o is dyadic-like Rational ) ) & ( for o being object holds
( o in D2 iff o is dyadic-like Rational ) ) implies D1 = D2 )
assume that
A2: for o being object holds
( o in D1 iff o is dyadic-like Rational ) and
A3: for o being object holds
( o in D2 iff o is dyadic-like Rational ) ; :: thesis: D1 = D2

now :: thesis: for o being object holds
( o in D1 iff o in D2 )

let o be object ; :: thesis: ( o in D1 iff o in D2 )
( o in D1 iff o is dyadic-like Rational ) by A2;
hence ( o in D1 iff o in D2 ) by A3; :: thesis: verum

end;

hence D1 = D2 by TARSKI:2; :: thesis: verum