
theorem Th2:
  for G being Group for h being set holds h in Subgroups G iff ex H
  being strict Subgroup of G st h = H
proof
  let G be Group;
  let h be set;
  thus h in Subgroups G implies ex H being strict Subgroup of G st h = H
  proof
    assume h in Subgroups G;
    then h is strict Subgroup of G by GROUP_3:def 1;
    hence thesis;
  end;
  thus thesis by GROUP_3:def 1;
end;
