thus ( X = Y implies for N being ExtNat holds
( N in X iff N in Y ) ) ; :: thesis: ( ( for N being ExtNat holds
( N in X iff N in Y ) ) implies X = Y )
assume for N being ExtNat holds
( N in X iff N in Y ) ; :: thesis: X = Y
then ( X c= Y & Y c= X ) ;
hence X = Y by XBOOLE_0:def 10; :: thesis: verum