let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for q, w, y, x being Element of L holds (((x | (y | (y | y))) | w) | ((q | q) | w)) | ((w | (x | q)) | (w | (x | q))) = w | (((x | q) | (x | q)) | (w | (x | q)))

now :: thesis: for y, p, w, q, x being Element of L holds (((x | (y | (y | y))) | w) | ((q | q) | w)) | ((w | (x | q)) | (w | (x | q))) = w | (((x | q) | (x | q)) | (w | (x | q)))

let y, p, w, q, x be Element of L; :: thesis: (((x | (y | (y | y))) | w) | ((q | q) | w)) | ((w | (x | q)) | (w | (x | q))) = w | (((x | q) | (x | q)) | (w | (x | q)))
(w | (p | (p | p))) | (w | (x | q)) = w by Th134;
hence (((x | (y | (y | y))) | w) | ((q | q) | w)) | ((w | (x | q)) | (w | (x | q))) = w | (((x | q) | (x | q)) | (w | (x | q))) by Th137; :: thesis: verum

end;

hence for q, w, y, x being Element of L holds (((x | (y | (y | y))) | w) | ((q | q) | w)) | ((w | (x | q)) | (w | (x | q))) = w | (((x | q) | (x | q)) | (w | (x | q))) ; :: thesis: verum