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

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

x | (y | y) = x | (x | y) by Th44;

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

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

x | (y | y) = x | (x | y) by Th44;

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