let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for w, q, z being Element of L holds ((w | w) | ((z | z) | q)) | ((q | ((q | q) | z)) | (q | ((q | q) | z))) = (((z | z) | q) | (w | q)) | (((z | z) | q) | (w | q))
let w, q, z be Element of L; :: thesis: ((w | w) | ((z | z) | q)) | ((q | ((q | q) | z)) | (q | ((q | q) | z))) = (((z | z) | q) | (w | q)) | (((z | z) | q) | (w | q))
(q | q) | ((z | z) | q) = (q | ((q | q) | z)) | (q | ((q | q) | z)) by Th74;
hence ((w | w) | ((z | z) | q)) | ((q | ((q | q) | z)) | (q | ((q | q) | z))) = (((z | z) | q) | (w | q)) | (((z | z) | q) | (w | q)) by SHEFFER1:def 15; :: thesis: verum