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

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

set X = x | (y | z);

set Y = y | x;

(x | (y | z)) | (y | x) = x by Th25;

hence (x | (y | z)) | (x | (u | (y | x))) = (x | (y | z)) | (y | x) by Th17; :: thesis: verum

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

set X = x | (y | z);

set Y = y | x;

(x | (y | z)) | (y | x) = x by Th25;

hence (x | (y | z)) | (x | (u | (y | x))) = (x | (y | z)) | (y | x) by Th17; :: thesis: verum