reserve a,a1,a2,v,v1,v2,x for object;
reserve V,A for set;
reserve m,n for Nat;
reserve S,S1,S2 for FinSequence;
reserve D,D1,D2 for NonatomicND of V,A;

theorem Th46:
  v in V & a in A implies ND_ex_1(v,a) is NonatomicND of V,A
  proof
    assume
A1: v in V & a in A;
    take S = <*NDSS(V,A)*>;
    thus S IsNDRankSeq V,A by Th27;
    ND_ex_1(v,a) in NDSS(V,A) by A1,Th45;
    hence thesis by FINSEQ_3:135;
  end;
