const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y const ZF_closed : set prop const Repl : set (set set) set axiom ZF_Repl_closed: !x:set.ZF_closed x -> !y:set.y iIn x -> !f:set set.(!z:set.z iIn y -> f z iIn x) -> Repl y f iIn x const Power : set set const If_i : prop set set set var x:set var y:set var z:set hyp ZF_closed x hyp y iIn x hyp z iIn x hyp Power (Power y) iIn x claim (!w:set.w iIn Power (Power y) -> If_i (y iIn w) y z iIn x) -> Repl (Power (Power y)) (\w:set.If_i (y iIn w) y z) iIn x