let L be non empty satisfying_Sh_1 ShefferStr ; :: thesis: for x, y, z being Element of L holds (x | (y | y)) | (x | (z | y)) = (x | (z | y)) | (x | (z | y))
let x, y, z be Element of L; :: thesis: (x | (y | y)) | (x | (z | y)) = (x | (z | y)) | (x | (z | y))
set Y = y;
set X = x;
(y | x) | x = x | (y | y) by Th43;
hence (x | (y | y)) | (x | (z | y)) = (x | (z | y)) | (x | (z | y)) by Th39; :: thesis: verum