reserve A,B,C,O for Ordinal,
        X for set,
        o for object,
        x,y,z,t,r,l for Surreal;
reserve n for Nat;

theorem Th50:
  x is uSurreal & y is uSurreal & x==y implies x=y
proof
  assume A1: x is uSurreal & y is uSurreal & x==y;
  thus x = Unique_No x by A1,Def11
  .= Unique_No y by A1,Th41
  .=y by A1,Def11;
end;
