reserve L for satisfying_Sh_1 non empty ShefferStr;
reserve L for satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3
  non empty ShefferStr;
reserve v,q,p,w,z,y,x for Element of L;

theorem Th116:
  for q,z,x holds (((q | ((x | x) | z)) | (q | ((x | x) | z))) |
  ((x | q) | ((z | z) | q))) = ((z | (x | q)) | ((q | q) | (x | q)))
proof
  let q,z,x;
  (z | z) | (z | z) = z by SHEFFER1:def 13;
  hence thesis by Th115;
end;
