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

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

let p, x, y be Element of L; :: thesis: y | (x | x) = (x | x) | y
((y | (x | x)) | (y | (x | x))) | (p | (p | p)) = y | (x | x) by Th71;
hence y | (x | x) = (x | x) | y by Th80; :: thesis: verum

end;

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