let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for z, p, q, y, x being Element of L holds q | (x | z) = (((z | z) | (p | (p | p))) | ((x | (y | (y | y))) | q)) | ((q | q) | ((x | (y | (y | y))) | q))
let z, p, q, y, x be Element of L; :: thesis: q | (x | z) = (((z | z) | (p | (p | p))) | ((x | (y | (y | y))) | q)) | ((q | q) | ((x | (y | (y | y))) | q))
(((x | (y | (y | y))) | q) | ((z | z) | q)) | ((q | (x | z)) | (q | (x | z))) = q | (x | z) by Th139;
hence q | (x | z) = (((z | z) | (p | (p | p))) | ((x | (y | (y | y))) | q)) | ((q | q) | ((x | (y | (y | y))) | q)) by Th140; :: thesis: verum