theorem Th73:
  for G,H being strict Group holds G,H are_isomorphic implies card G = card H
proof
  let G,H be strict Group;
  assume
A1: G,H are_isomorphic;
  then consider h being Homomorphism of G,H such that
A2: h is bijective;
  consider g1 being Homomorphism of H,G such that
A3: g1 is bijective by A1,Def11;
  Image g1 = G by A3,Th57;
  then
A4: card G c= card H by Th52;
  Image h = H by A2,Th57;
  hence thesis by A4,Th52;
end;
