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

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

set Y = y | (x | z);

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

hence (x | (y | (x | z))) | y = y | (x | z) by Th24; :: thesis: verum

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

set Y = y | (x | z);

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

hence (x | (y | (x | z))) | y = y | (x | z) by Th24; :: thesis: verum