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 | ((x | x) | q)) | ((q | q) | ((x | x) | q))
let q, z, x be Element of L; :: thesis: q | (x | z) = (z | ((x | x) | q)) | ((q | q) | ((x | x) | q))
(z | z) | (z | z) = z by SHEFFER1:def 13;
hence q | (x | z) = (z | ((x | x) | q)) | ((q | q) | ((x | x) | q)) by Th99; :: thesis: verum