theorem Th107:
  for H1,H2 being strict Subgroup of G holds H1 in con_class H2
  iff H1,H2 are_conjugated
proof
  let H1,H2 be strict Subgroup of G;
  thus H1 in con_class H2 implies H1,H2 are_conjugated
  proof
    assume H1 in con_class H2; then
    ex H3 being strict Subgroup of G st H1 = H3 & H2,H3 are_conjugated by Def12
;
    hence thesis;
  end;
  assume H1,H2 are_conjugated;
  hence thesis by Def12;
end;
