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

hence
for x, q, y being Element of L holds (x | y) | (x | (y | q)) = x
; :: thesis: verumlet 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;(x | y) | (x | (y | (z | (z | z)))) = x by Th112;

hence (x | y) | (x | (y | q)) = x by Th159; :: thesis: verum