let L be non empty satisfying_Sh_1 ShefferStr ; :: thesis: for x, y, z being Element of L holds ((x | (y | z)) | (x | (y | z))) | (y | y) = x | (y | y)

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

set Z = y | y;

set Y = y | z;

(x | (y | z)) | (x | (y | z)) = (x | (y | z)) | (x | (y | y)) by Th46;

hence ((x | (y | z)) | (x | (y | z))) | (y | y) = x | (y | y) by Th26; :: thesis: verum

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

set Z = y | y;

set Y = y | z;

(x | (y | z)) | (x | (y | z)) = (x | (y | z)) | (x | (y | y)) by Th46;

hence ((x | (y | z)) | (x | (y | z))) | (y | y) = x | (y | y) by Th26; :: thesis: verum