reserve x,y for set;

theorem Th19:
  for F being Field-like Abelian distributive add-associative
right_zeroed right_complementable non degenerated doubleLoopStr, a,b,c being
  Element of F holds (a*b)*c = a*(b*c)
proof
  let F be Field-like Abelian distributive add-associative right_zeroed
  right_complementable non degenerated doubleLoopStr, a,b,c be Element of
  suppf1(F);
  a = 0.F or b = 0.F or c = 0.F or a is Element of NonZero F & b is
  Element of NonZero F & c is Element of NonZero F by ZFMISC_1:56;
  hence thesis by Th4;
end;
