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 Th92:
  {a},{b} are_conjugated iff a,b are_conjugated
proof
  thus {a},{b} are_conjugated implies a,b are_conjugated
  proof
    assume {a},{b} are_conjugated;
    then consider g such that
A1: {a} |^ g = {b} by Th88;
    {b} = {a |^ g} by A1,Th37;
    then b = a |^ g by ZFMISC_1:3;
    hence thesis by Th74;
  end;
  assume a,b are_conjugated;
  then consider g such that
A2: a |^ g = b by Th74;
  {b} = {a} |^ g by A2,Th37;
  hence thesis by Th88;
end;
