let x be set ; :: thesis: for A being Ordinal holds
( x in Rank A iff {x} in Rank (succ A) )
let A be Ordinal; :: thesis: ( x in Rank A iff {x} in Rank (succ A) )
( ( x in Rank A implies {x} c= Rank A ) & ( {x} c= Rank A implies x in Rank A ) & ( {x} c= Rank A implies {x} in Rank (succ A) ) & ( {x} in Rank (succ A) implies {x} c= Rank A ) ) by Th36, ZFMISC_1:37;
hence ( x in Rank A iff {x} in Rank (succ A) ) ; :: thesis: verum