const PNo_rel_strict_upperbd : (set (set prop) prop) set (set prop) prop const PNo_rel_strict_lowerbd : (set (set prop) prop) set (set prop) prop term PNo_rel_strict_imv = \P:set (set prop) prop.\Q:set (set prop) prop.\x:set.\p:set prop.PNo_rel_strict_upperbd P x p & PNo_rel_strict_lowerbd Q x p const ordinal : set prop const PNoEq_ : set (set prop) (set prop) prop axiom PNoEq_rel_strict_upperbd: !P:set (set prop) prop.!x:set.ordinal x -> !p:set prop.!q:set prop.PNoEq_ x p q -> PNo_rel_strict_upperbd P x p -> PNo_rel_strict_upperbd P x q axiom PNoEq_rel_strict_lowerbd: !P:set (set prop) prop.!x:set.ordinal x -> !p:set prop.!q:set prop.PNoEq_ x p q -> PNo_rel_strict_lowerbd P x p -> PNo_rel_strict_lowerbd P x q claim !P:set (set prop) prop.!Q:set (set prop) prop.!x:set.ordinal x -> !p:set prop.!q:set prop.PNoEq_ x p q -> PNo_rel_strict_imv P Q x p -> PNo_rel_strict_upperbd P x q & PNo_rel_strict_lowerbd Q x q