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