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

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