theorem
  [x,y] in [:X,{z}:] iff x in X & y = z
proof
A1: y in {z} iff y=z by TARSKI:def 1;
  hence [x,y] in [:X,{z}:] implies x in X & y=z by Lm16;
  thus thesis by A1,Lm16;
end;
