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 Th77:
  a,b are_conjugated & b,c are_conjugated implies a,c are_conjugated
proof
  given g such that
A1: a = b |^ g;
  given h such that
A2: b = c |^ h;
  a = c |^ (h * g) by A1,A2,Th24;
  hence thesis;
end;
