const Union : set set const UPair : set set set term binunion = \x:set.\y:set.Union (UPair x y) const In : set set prop term iIn = In infix iIn 2000 2000 axiom UPairI2: !x:set.!y:set.y iIn UPair x y axiom UnionI: !x:set.!y:set.!z:set.y iIn z -> z iIn x -> y iIn Union x claim !x:set.!y:set.!z:set.z iIn y -> z iIn binunion x y