let L be non empty satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 ShefferStr ; :: thesis: for x, z, y being Element of L holds ((x | ((y | y) | z)) | (x | ((y | y) | z))) | ((y | x) | ((z | z) | x)) = (z | (y | x)) | x
let x, z, y be Element of L; :: thesis: ((x | ((y | y) | z)) | (x | ((y | y) | z))) | ((y | x) | ((z | z) | x)) = (z | (y | x)) | x
(x | x) | (y | x) = x by Th121;
hence ((x | ((y | y) | z)) | (x | ((y | y) | z))) | ((y | x) | ((z | z) | x)) = (z | (y | x)) | x by Th116; :: thesis: verum