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 Th117:
  for w,q,z holds (((w | w) | ((z | z) | q)) | ((q | ((q | q) | z
)) | (q | ((q | q) | z)))) = (((z | z) | q) | (w | q)) | (((z | z) | q) | (w |
  q))
proof
  let w,q,z;
  (q | q) | ((z | z) | q) = ((q | ((q | q) | z)) | (q | ((q | q) | z))) by Th74
;
  hence thesis by SHEFFER1:def 15;
end;
