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

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

x | (y | (x | x)) = x | x by Th12;

hence x | (y | (y | (z | (x | y)))) = x | x by Th57; :: thesis: verum

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

x | (y | (x | x)) = x | x by Th12;

hence x | (y | (y | (z | (x | y)))) = x | x by Th57; :: thesis: verum