set A = {} T;

take {} T ; :: thesis: ( {} T is condensed & {} T is subcondensed & {} T is supercondensed )

( {} T is supercondensed & {} T is subcondensed ) ;

hence ( {} T is condensed & {} T is subcondensed & {} T is supercondensed ) ; :: thesis: verum

take {} T ; :: thesis: ( {} T is condensed & {} T is subcondensed & {} T is supercondensed )

( {} T is supercondensed & {} T is subcondensed ) ;

hence ( {} T is condensed & {} T is subcondensed & {} T is supercondensed ) ; :: thesis: verum