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)) | z = z | (y | x)

let x, z, y be Element of L; :: thesis: (x | ((y | y) | z)) | z = z | (y | x)

(z | z) | ((y | y) | z) = z by Th121;

hence (x | ((y | y) | z)) | z = z | (y | x) by Th100; :: thesis: verum

let x, z, y be Element of L; :: thesis: (x | ((y | y) | z)) | z = z | (y | x)

(z | z) | ((y | y) | z) = z by Th121;

hence (x | ((y | y) | z)) | z = z | (y | x) by Th100; :: thesis: verum