reserve x,y,y1,y2 for set;
reserve G for Group;
reserve a,b,c,d,g,h for Element of G;
reserve A,B,C,D for Subset of G;
reserve H,H1,H2,H3 for Subgroup of G;
reserve n for Nat;
reserve i for Integer;

theorem Th93:
  A,carr H1 are_conjugated implies ex H2 being strict Subgroup of
  G st the carrier of H2 = A
proof
  assume A,carr H1 are_conjugated;
  then consider g such that
A1: A = carr H1 |^ g;
  A = the carrier of H1 |^ g by A1,Def6;
  hence thesis;
end;
