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

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

x | (y | (z | (x | y))) = x | (y | ((y | x) | z)) by Th37;

hence x | (y | ((y | x) | z)) = x | (y | y) by Th38; :: thesis: verum

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

x | (y | (z | (x | y))) = x | (y | ((y | x) | z)) by Th37;

hence x | (y | ((y | x) | z)) = x | (y | y) by Th38; :: thesis: verum