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)
let q, w, y, 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) | (x | q)) | (w | (x | q)) = x | q by Th121;
hence (((x | (y | (y | y))) | w) | ((q | q) | w)) | ((w | (x | q)) | (w | (x | q))) = w | (x | q) by Th138; :: thesis: verum