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 (((y | y) | z) | (x | z)) | (((y | y) | z) | (x | z)) = ((x | x) | ((y | y) | z)) | z
let x, z, y be Element of L; :: thesis: (((y | y) | z) | (x | z)) | (((y | y) | z) | (x | z)) = ((x | x) | ((y | y) | z)) | z
(z | ((z | z) | y)) | (z | ((z | z) | y)) = z by Th128;
hence (((y | y) | z) | (x | z)) | (((y | y) | z) | (x | z)) = ((x | x) | ((y | y) | z)) | z by Th117; :: thesis: verum