let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for z, p, q, y, x being Element of L holds (((x | (y | (y | y))) | q) | ((z | z) | q)) | ((q | (x | z)) | (q | (x | z))) = (((z | z) | (p | (p | p))) | ((x | (y | (y | y))) | q)) | ((q | q) | ((x | (y | (y | y))) | q))
let z, p, q, y, x be Element of L; :: thesis: (((x | (y | (y | y))) | q) | ((z | z) | q)) | ((q | (x | z)) | (q | (x | z))) = (((z | z) | (p | (p | p))) | ((x | (y | (y | y))) | q)) | ((q | q) | ((x | (y | (y | y))) | q))
((x | (y | (y | y))) | q) | ((z | z) | q) = (q | (x | z)) | (q | (x | z)) by Th73;
hence (((x | (y | (y | y))) | q) | ((z | z) | q)) | ((q | (x | z)) | (q | (x | z))) = (((z | z) | (p | (p | p))) | ((x | (y | (y | y))) | q)) | ((q | q) | ((x | (y | (y | y))) | q)) by Th73; :: thesis: verum