const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y const Repl : set (set set) set const Power : set set const Empty : set const If_i : prop set set set term UPair = \x:set.\y:set.Repl (Power (Power Empty)) \z:set.If_i (Empty iIn z) x y axiom EmptyE: !x:set.nIn x Empty axiom Empty_In_Power: !x:set.Empty iIn Power x axiom ReplI: !x:set.!f:set set.!y:set.y iIn x -> f y iIn Repl x f axiom If_i_0: !P:prop.!x:set.!y:set.~ P -> If_i P x y = y claim !x:set.!y:set.y iIn UPair x y