reserve A,B,C for Ordinal,
  X,X1,Y,Y1,Z for set,a,b,b1,b2,x,y,z for object,
  R for Relation,
  f,g,h for Function,
  k,m,n for Nat;
reserve M,N for Cardinal;
reserve S for Sequence;
reserve k,n,m for Nat;
reserve l for Element of omega;

theorem Th63:
 for X being non empty set, A being Singleton of X
  ex x being Element of X st A = {x}
  proof let X be non empty set, A be Singleton of X;
    consider x being object such that
A1:   A = {x} by ZFMISC_1:131;
    x in A by A1,TARSKI:def 1;
    then reconsider x as Element of X;
   take x;
   thus thesis by A1;
  end;
