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 Th74:
  a,b are_conjugated iff ex g st b = a |^ g
proof
  thus a,b are_conjugated implies ex g st b = a |^ g
  proof
    given g such that
A1: a = b |^ g;
    a |^ g" = b by A1,Th25;
    hence thesis;
  end;
  given g such that
A2: b = a |^ g;
  a = b |^ g" by A2,Th25;
  hence thesis;
end;
