reserve F,H,H9 for ZF-formula,
  x,y,z,t for Variable,
  a,b,c,d,A,X for set;
reserve E for non empty set,
  f,g,h for Function of VAR,E,
  v1,v2,v3,v4,v5,u5 for Element of VAL E;

theorem
  H is being_membership implies for f holds f.(Var1 H) in f.(Var2 H) iff
  f in St(H,E)
proof
  assume H is being_membership;
  then H = (Var1 H) 'in' Var2 H by ZF_LANG:37;
  hence thesis by Th3;
end;
