let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for q, z, x being Element of L holds ((q | ((x | x) | z)) | (q | ((x | x) | z))) | ((x | q) | ((z | z) | q)) = (z | (x | q)) | ((q | q) | (x | q))
let q, z, x be Element of L; :: thesis: ((q | ((x | x) | z)) | (q | ((x | x) | z))) | ((x | q) | ((z | z) | q)) = (z | (x | q)) | ((q | q) | (x | q))
(z | z) | (z | z) = z by SHEFFER1:def 13;
hence ((q | ((x | x) | z)) | (q | ((x | x) | z))) | ((x | q) | ((z | z) | q)) = (z | (x | q)) | ((q | q) | (x | q)) by Th115; :: thesis: verum