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 | z) = (((z | z) | (z | z)) | ((x | x) | q)) | ((q | q) | ((x | x) | q))
let q, z, x be Element of L; :: thesis: q | (x | z) = (((z | z) | (z | z)) | ((x | x) | q)) | ((q | q) | ((x | x) | q))
(((x | x) | q) | ((z | z) | q)) | ((q | (x | z)) | (q | (x | z))) = q | (x | z) by Th94;
hence q | (x | z) = (((z | z) | (z | z)) | ((x | x) | q)) | ((q | q) | ((x | x) | q)) by Th98; :: thesis: verum