
theorem Th14:
  for a1,b1,a2,b2,a3,b3 being set st compsym(a1,a2,a3) = compsym(
  b1,b2,b3) holds a1 = b1 & a2 = b2 & a3 = b3
proof
  let a1,b1,a2,b2,a3,b3 be set;
A1: <*a1,a2,a3*>.3 = a3;
  assume compsym(a1,a2,a3) = compsym(b1,b2,b3);
  then
A2: <*a1,a2,a3*> = <*b1,b2,b3*> by XTUPLE_0:1;
  <*a1,a2,a3*>.1 = a1 & <*a1,a2,a3*>.2 = a2;
  hence thesis by A2,A1,FINSEQ_1:45;
end;
