
theorem Th2:
  for x,y being set st <*x,y*> is constant holds x = y
proof
  let x,y be set;
A1: rng<*x,y*> = rng(<*x*>^<*y*>) by FINSEQ_1:def 9
    .= rng<*x*> \/ rng<*y*> by FINSEQ_1:31
    .= rng<*x*> \/ {y} by FINSEQ_1:38
    .= {x} \/ {y}by FINSEQ_1:38
    .= {x,y} by ENUMSET1:1;
A2: y in {x,y} by TARSKI:def 2;
  assume <*x,y*> is constant;
  then reconsider s = <*x,y*> as constant Function;
A3: x in {x,y} by TARSKI:def 2;
  rng s is trivial;
  hence thesis by A1,A3,A2,ZFMISC_1:def 10;
end;
