const In : set set prop term iIn = In infix iIn 2000 2000 term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y term TransSet = \x:set.!y:set.y iIn x -> Subq y x term ordinal = \x:set.TransSet x & !y:set.y iIn x -> TransSet y const famunion : set (set set) set axiom famunionI: !x:set.!f:set set.!y:set.!z:set.y iIn x -> z iIn f y -> z iIn famunion x f var x:set var f:set set var y:set var z:set var w:set hyp z iIn x hyp y iIn f z hyp TransSet (f z) hyp w iIn y claim w iIn f z -> w iIn famunion x f