reserve x,y for set;

theorem Th20:
  for F being Field-like Abelian distributive add-associative
  right_zeroed right_complementable non degenerated doubleLoopStr, a,b being
  Element of F holds a*b = b*a
proof
  let F be Field-like Abelian distributive add-associative right_zeroed
right_complementable non degenerated doubleLoopStr, a,b be Element of suppf1(
  F);
  a = 0.F or b = 0.F or a is Element of NonZero F & b is Element of
  NonZero F by ZFMISC_1:56;
  hence thesis by Th5;
end;
