const Union : set set const Repl : set (set set) set term famunion = \x:set.\f:set set.Union (Repl x f) const In : set set prop term iIn = In infix iIn 2000 2000 axiom ReplE_impred: !x:set.!f:set set.!y:set.y iIn Repl x f -> !P:prop.(!z:set.z iIn x -> y = f z -> P) -> P axiom UnionE_impred: !x:set.!y:set.y iIn Union x -> !P:prop.(!z:set.y iIn z -> z iIn x -> P) -> P claim !x:set.!f:set set.!y:set.y iIn famunion x f -> ?z:set.z iIn x & y iIn f z