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

now :: thesis: for p, z, q, y, x being Element of L holds q | (x | z) = (z | ((x | (y | (y | y))) | q)) | ((q | q) | ((x | (y | (y | y))) | q))

let p, z, q, y, x be Element of L; :: thesis: q | (x | z) = (z | ((x | (y | (y | y))) | q)) | ((q | q) | ((x | (y | (y | y))) | q))
(z | z) | (p | (p | p)) = z by Th71;
hence q | (x | z) = (z | ((x | (y | (y | y))) | q)) | ((q | q) | ((x | (y | (y | y))) | q)) by Th141; :: thesis: verum

end;

hence for z, q, y, x being Element of L holds q | (x | z) = (z | ((x | (y | (y | y))) | q)) | ((q | q) | ((x | (y | (y | y))) | q)) ; :: thesis: verum