reserve n for Element of NAT;
reserve i for Integer;
reserve G,H,I for Group;
reserve A,B for Subgroup of G;
reserve N for normal Subgroup of G;
reserve a,a1,a2,a3,b,b1 for Element of G;
reserve c,d for Element of H;
reserve f for Function of the carrier of G, the carrier of H;
reserve x,y,y1,y2,z for set;
reserve A1,A2 for Subset of G;
reserve N for normal Subgroup of G;
reserve S,T1,T2 for Element of G./.N;
reserve g,h for Homomorphism of G,H;
reserve h1 for Homomorphism of H,I;

theorem Th66:
  for G,H being Group holds G,H are_isomorphic implies
  H,G are_isomorphic
proof
  let G,H be Group;
  assume G,H are_isomorphic;
  then consider h being Homomorphism of G,H such that
A1: h is bijective;
  reconsider g = h" as Homomorphism of H,G by A1,Th62;
  take g;
  thus thesis by A1,Th63;
end;
