reserve A,B,C for Ordinal,
  X,X1,Y,Y1,Z for set,a,b,b1,b2,x,y,z for object,
  R for Relation,
  f,g,h for Function,
  k,m,n for Nat;
reserve M,N for Cardinal;

theorem Th10:
  X c= Y implies card X c= card Y
proof
  assume
A1: X c= Y;
  ex f st f is one-to-one & dom f = X & rng f c= Y
  proof
    take id X;
    thus thesis by A1,RELAT_1:45;
  end;
  hence thesis by Th9;
end;
