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

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

set Y = y | x;

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

hence x | (y | (x | (y | z))) = x | (y | z) by Th25; :: thesis: verum

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

set Y = y | x;

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

hence x | (y | (x | (y | z))) = x | (y | z) by Th25; :: thesis: verum