let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; 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 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;
(((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;
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)))
; verum