reserve E,X,Y,x for set;
reserve A,B,C for Subset of E;

theorem Th4:
  A <> {} implies ex x being Element of E st x in A
proof
  assume A <> {};
  then consider x being object such that
A1: x in A by XBOOLE_0:def 1;
  reconsider x as set by TARSKI:1;
  x in E by A1,Lm1;
  then x is Element of E by Def1;
  hence thesis by A1;
end;
