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

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

let q, x, z, y be Element of L; :: thesis: (x | y) | (x | (y | q)) = x
(x | y) | (x | (y | (z | (z | z)))) = x by Th112;
hence (x | y) | (x | (y | q)) = x by Th159; :: thesis: verum

end;

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