theorem
  for A being set,X being non empty set,S being a_partition of X holds A
  in S implies ex x being Element of X st A = EqClass(x,S)
proof
  let A be set,X be non empty set,S be a_partition of X;
  assume
A1: A in S;
  then A is non empty by Def4;
  then consider x being object such that
A2: x in A;
  take x;
  thus thesis by A1,A2,Def6;
end;
