reserve m for Cardinal,
  A,B,C for Ordinal,
  x,y,z,X,Y,Z,W for set,
  f for Function;
reserve f,g for Function,
  L for Sequence,
  F for Cardinal-Function;
reserve U1,U2,U for Universe;
reserve u,v for Element of U;

theorem
  UNIVERSE A = UNIVERSE B implies A = B
proof
  assume that
A1: UNIVERSE A = UNIVERSE B and
A2: A <> B;
  A in B or B in A by A2,ORDINAL1:14;
  then UNIVERSE A in UNIVERSE B or UNIVERSE B in UNIVERSE A by Th70;
  hence contradiction by A1;
end;
