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

theorem
  x - y == 0_No implies x == y
proof
A1: -y+y=y-y ==0_No by Th39;
  assume x - y == 0_No;
  then y = 0_No+ y == x + - y + y = x + (- y + y) by Th37,Th43;
  then y == x +(-y+y) == x+0_No =x by A1,Th43;
  hence thesis by SURREALO:4;
end;
