const In : set set prop term iIn = In infix iIn 2000 2000 term PNoEq_ = \x:set.\p:set prop.\q:set prop.!y:set.y iIn x -> (p y <-> q y) term SNoEq_ = \x:set.\y:set.\z:set.PNoEq_ x (\w:set.w iIn y) \w:set.w iIn z const Subq : set set prop axiom Subq_ref: !x:set.Subq x x const SNo : set prop const SNoLev : set set axiom SNo_Subq: !x:set.!y:set.SNo x -> SNo y -> Subq (SNoLev x) (SNoLev y) -> (!z:set.z iIn SNoLev x -> (z iIn x <-> z iIn y)) -> Subq x y axiom iff_sym: !P:prop.!Q:prop.(P <-> Q) -> (Q <-> P) axiom set_ext: !x:set.!y:set.Subq x y -> Subq y x -> x = y claim !x:set.!y:set.SNo x -> SNo y -> SNoLev x = SNoLev y -> SNoEq_ (SNoLev x) x y -> x = y